%
% reference list for article lrr-2002-6 created at 2016-10-26T21:12:39
%
% note: the URLs in this bibtex database may contain characters which will be
% interpreted incorrectly by tex, unless used as argument of a \url command (or
% an equivalent).
@book{alinhac91,
address = {Les Ulis, France},
author = {Alinhac, S. and G{\'{e}}rard, P.},
gbs_id = {kLT0dL86sM8C},
keywords = {Nonlinear analysis, Littlewood-Paley theory},
publisher = {EDP Sciences},
series = {Savoirs Actuels},
title = {Op\'{e}rateurs pseudo-diff\'{e}rentiels et Th\'{e}or\`{e}me de Nash--Moser},
year = {1991}
}
@article{andersson92,
author = {Andersson, L. and Chru{\'{s}}ciel, P. T. and Friedrich, H.},
doi = {10.1007/BF02096944},
journal = {Commun. Math. Phys.},
keywords = {Einstein constraints, Constraint equations, Hyperboloidal data, Yamabe problem},
pages = {587--612},
title = {On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations},
volume = {149},
year = {1992}
}
@incollection{anderson97a,
address = {Cambridge, U.K.; New York, U.S.A.},
author = {Anderson, M. T.},
booktitle = {Comparison Geometry},
editor = {Grove, K. and Peterson, P.},
gbs_id = {OZtOkxCji-EC},
keywords = {Geometrization, Scalar curvature},
pages = {49--82},
publisher = {Cambridge University Press},
series = {Mathematical Sciences Research Institute Publications},
title = {Scalar curvature and geometrization structures for 3-manifolds},
volume = {30},
year = {1997}
}
@article{andersson97a,
author = {Andersson, L. and Moncrief, V. and Tromba, A.},
doi = {10.1016/S0393-0440(97)87804-7},
journal = {J. Geom. Phys.},
keywords = {Einstein equations, Vacuum, 2+1 gravity},
pages = {191--205},
title = {On the global evolution problem in 2+1 gravity},
volume = {23},
year = {1997}
}
@preprint{andersson99a,
author = {Andersson, L.},
cited = {4 December 1999},
eid = {gr-qc/9911032},
format = {arxiv},
keywords = {Existence theorems, Einstein equations, Stability, Stability theory},
month = {November},
title = {The global existence problem in general relativity},
url = {http://arXiv.org/abs/gr-qc/9911032},
year = {1999}
}
@article{andersson01a,
author = {Andersson, L. and Rendall, A. D.},
doi = {10.1007/s002200100406},
eprint = {gr-qc/0001047},
journal = {Commun. Math. Phys.},
keywords = {Singularities, Fuchsian equation, Scalar fields},
pages = {479--511},
title = {Quiescent cosmological singularities},
volume = {218},
year = {2001}
}
@article{andreasson96,
author = {Andr{\'{e}}asson, H.},
doi = {10.1137/0527076},
journal = {SIAM J. Math. Anal.},
keywords = {Boltzmann equation},
pages = {1386--1405},
title = {Regularity of the gain term and strong $L^1$ convergence to equilibrium for the relativistic Boltzmann equation},
volume = {27},
year = {1996}
}
@article{andreasson99,
author = {Andr{\'{e}}asson, H.},
doi = {10.1007/s002200050708},
eprint = {gr-qc/9812035},
journal = {Commun. Math. Phys.},
keywords = {Vlasov equation, Cosmology},
pages = {337--365},
title = {Global foliations of matter spacetimes with Gowdy symmetry},
volume = {206},
year = {1999}
}
@article{andreasson01a,
author = {Andr{\'{e}}asson, H. and Rein, G. and Rendall, A. D.},
cited = {28 January 2002},
journal = {Math. Proc. Camb. Phil. Soc.},
keywords = {Hyperbolic symmetry, Vlasov equation},
pages = {529--549},
title = {On the Einstein--Vlasov system with hyperbolic symmetry},
volume = {134},
year = {2001}
}
@article{anguige99a,
author = {Anguige, K. and Tod, K. P.},
doi = {10.1006/aphy.1999.5946},
journal = {Ann. Phys. (N.Y.)},
keywords = {Euler equations, Cosmology, Isotropic singularities},
pages = {257--293},
title = {Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes},
volume = {276},
year = {1999}
}
@article{anguige99b,
author = {Anguige, K. and Tod, K. P.},
doi = {10.1006/aphy.1999.5947},
journal = {Ann. Phys. (N.Y.)},
keywords = {Vlasov equation, Cosmology, Isotropic singularities},
pages = {294--320},
title = {Isotropic Cosmological Singularities II. The Einstein--Vlasov System},
volume = {276},
year = {1999}
}
@article{anguige00a,
author = {Anguige, K.},
doi = {10.1088/0264-9381/17/10/306},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Singularities, Cosmology, Euler equations},
pages = {2117--2128},
title = {A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity},
volume = {17},
year = {2000}
}
@article{anguige00b,
author = {Anguige, K.},
doi = {10.1006/aphy.2000.6037},
journal = {Ann. Phys. (N.Y.)},
keywords = {Einstein equations, Singularities, Cosmology, Vlasov equation},
pages = {395--419},
title = {Isotropic Cosmological Singularities. III. The Cauchy Problem for the Inhomogeneous Conformal Einstein--Vlasov Equations},
volume = {282},
year = {2000}
}
@preprint{anguige00c,
author = {Anguige, K.},
cited = {29 January 2002},
eid = {gr-qc/0005086},
format = {arxiv},
keywords = {Einstein equations, Singularities, Cosmology, Euler equations},
month = {May},
title = {A class of perfect-fluid cosmologies with polarised Gowdy symmetry and a Kasner-like singularity},
url = {http://arXiv.org/abs/gr-qc/0005086},
year = {2000}
}
@article{anninos01a,
author = {Anninos, P.},
cited = {24 January 2002},
eid = {lrr-2001-2},
journal = {Living Rev. Relativity},
keywords = {Cosmology, Numerical relativity},
title = {Computational Cosmology: From the Early Universe to the Large Scale Structure},
url = {http://www.livingreviews.org/lrr-2001-2},
volume = {4},
year = {2001}
}
@article{arkeryd92,
author = {Arkeryd, L.},
journal = {Stud. Appl. Math.},
keywords = {Boltzmann equation},
pages = {283--288},
title = {On the strong $L^1$ trend to equilibrium for the Boltzmann equation},
volume = {87},
year = {1992}
}
@incollection{arnold88,
address = {Berlin, Germany; New York, U.S.A.},
author = {Arnold, V. I. and Ilyashenko, Y. S.},
booktitle = {Dynamical Systems I: Ordinary Differential Equations and Smooth Dynamical Systems},
editor = {Anosov, D. V. and Arnold, V. I.},
keywords = {Dynamical systems, Ordinary differential equations},
pages = {1--148},
publisher = {Springer},
series = {Encyclopaedia of Mathematical Sciences},
title = {Ordinary differential equations},
volume = {1},
year = {1988}
}
@book{aubin82,
address = {Berlin, Germany; New York, U.S.A.},
author = {Aubin, T.},
gbs_id = {NcLiTzEwFbcC},
keywords = {Nonlinear analysis, Sobolev spaces},
publisher = {Springer},
series = {Grundlehren der mathematischen Wissenschaften},
title = {Nonlinear Analysis on Manifolds. Monge--Amp\`{e}re equations},
volume = {252},
year = {1982}
}
@article{baouendi77,
author = {Baouendi, M. S. and Goulaouic, C.},
doi = {10.1080/03605307708820057},
journal = {Commun. Part. Diff. Eq.},
keywords = {Fuchsian equation, Singularities},
pages = {1151--1162},
title = {Remarks on the abstract form of nonlinear Cauchy--Kovalevsky theorems},
volume = {2},
year = {1977}
}
@article{barrow01a,
author = {Barrow, J. D. and Kodama, H.},
doi = {10.1142/S0218271801001554},
journal = {Int. J. Mod. Phys. D},
keywords = {Cosmology},
pages = {785--790},
title = {All universes great and small},
volume = {10},
year = {2001}
}
@article{bartnik88a,
author = {Bartnik, R.},
doi = {10.1007/BF01218388},
journal = {Commun. Math. Phys.},
keywords = {Cosmological spacetimes, Constant mean curvature hypersurfaces},
pages = {615--624},
title = {Remarks on cosmological spacetimes and constant mean curvature hypersurfaces},
volume = {117},
year = {1988}
}
@article{bartnik93a,
author = {Bartnik, R.},
journal = {J. Differ. Geom.},
keywords = {Einstein constraints, Constraint equations},
pages = {31--71},
title = {Quasi-spherical metrics and prescribed scalar curvature},
volume = {37},
year = {1993}
}
@article{bartnik93b,
author = {Bartnik, R. and Fodor, G.},
journal = {Phys. Rev. D},
keywords = {Constraints},
pages = {3596--3599},
title = {On the restricted validity of the thin sandwich conjecture},
volume = {48},
year = {1993}
}
@article{bartnik88b,
author = {Bartnik, R. and McKinnon, J.},
doi = {10.1103/PhysRevLett.61.141},
journal = {Phys. Rev. Lett.},
keywords = {Einstein-Yang-Mills equations, Bartnik-McKinnon solutions},
pages = {141--144},
title = {Particlelike Solutions of the Einstein--Yang--Mills Equations},
volume = {61},
year = {1988}
}
@article{batt86,
author = {Batt, J. and Faltenbacher, W. and Horst, E.},
doi = {10.1007/BF00279958},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Vlasov equation, Stellar dynamics},
pages = {159--183},
title = {Stationary Spherically Symmetric Models in Stellar Dynamics},
volume = {93},
year = {1986}
}
@article{beale93,
author = {Beale, J. T. and Hou, T. Y. and Lowengrub, J. S.},
doi = {10.1002/cpa.3160460903},
journal = {Commun. Pure Appl. Math.},
keywords = {Fluids, Free boundary},
pages = {1269--1301},
title = {Growth rates for the linearized motion of fluid interfaces away from equilibrium},
volume = {46},
year = {1993}
}
@article{beig02a,
author = {Beig, R. and Schmidt, B. G.},
cited = {8 February 2002},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Elasticity},
pages = {109--115},
title = {Static, self-gravitating elastic bodies},
volume = {459},
year = {2002}
}
@article{belinskii70,
author = {Belinskii, V. A. and Khalatnikov, I. M. and Lifshitz, E. M.},
doi = {10.1080/00018737000101171},
journal = {Adv. Phys.},
keywords = {Singularities},
pages = {525--573},
title = {Oscillatory Approach to a Singular Point in the Relativistic Cosmology},
volume = {19},
year = {1970}
}
@article{belinskii82,
author = {Belinskii, V. A. and Khalatnikov, I. M. and Lifshitz, E. M.},
doi = {10.1080/00018738200101428},
journal = {Adv. Phys.},
keywords = {Singularities},
pages = {639--667},
title = {A general solution of the Einstein equations with a time singularity},
volume = {31},
year = {1982}
}
@article{belinskii86a,
author = {Belinskii, V. A. and Grishchuk, L. P. and Zel'dovich, Y. B. and Khalatnikov, I. M.},
journal = {Sov. Phys. JETP},
keywords = {Inflation, Scalar fields},
pages = {195--203},
title = {Inflationary stages in cosmological models with a scalar field},
volume = {62},
year = {1986}
}
@article{belinskii92a,
author = {Belinskii, V. A.},
journal = {JETP Lett.},
keywords = {Singularities, Cosmology},
pages = {421--425},
title = {Turbulence of a gravitational field near a cosmological singularity},
volume = {56},
year = {1992}
}
@article{berger97,
author = {Berger, B. K. and Chru{\'{s}}ciel, P. T. and Isenberg, J. and Moncrief, V.},
doi = {10.1006/aphy.1997.5707},
eprint = {gr-qc/9702007},
journal = {Ann. Phys. (N.Y.)},
keywords = {Time foliations, T2 symmetry, Global existence},
pages = {117--148},
title = {Global Foliations of Vacuum Spacetimes with $T^{2}$ Isometry},
volume = {260},
year = {1997}
}
@article{berger95,
archiveprefix = {arXiv},
author = {Berger, B. K. and Chru{\'{s}}ciel, P. T. and Moncrief, V.},
doi = {10.1006/aphy.1995.1012},
eprint = {gr-qc/9404005},
journal = {Ann. Phys. (N.Y.)},
keywords = {Global existence, Cylindrical symmetry},
pages = {322--354},
title = {On `Asymptotically Flat' Space-Times with $G_2$-Invariant Cauchy Surfaces},
volume = {237},
year = {1995}
}
@article{berger00a,
author = {Berger, B. K. and Moncrief, V.},
eid = {023509},
journal = {Phys. Rev. D},
keywords = {Mixmaster},
pages = {1--8},
title = {Exact U(1) symmetric cosmologies with local Mixmaster dynamics},
volume = {62},
year = {2000}
}
@article{berger02a,
author = {Berger, B. K.},
cited = {28 January 2002},
eid = {lrr-2002-1},
journal = {Living Rev. Relativity},
keywords = {Singularities, Cosmology, Numerical relativity},
title = {Numerical Approaches to Spacetime Singularities},
url = {http://www.livingreviews.org/lrr-2002-1},
volume = {5},
year = {2002}
}
@article{beyer95,
author = {Beyer, H.},
journal = {J. Math. Phys.},
keywords = {Stars, Euler equations, Stability, Stability theory},
pages = {4792--4814},
title = {The spectrum of adiabatic stellar oscillations},
volume = {36},
year = {1995}
}
@article{beyer01,
author = {Beyer, H.},
doi = {10.1007/s002200100494},
journal = {Commun. Math. Phys.},
keywords = {Kerr solution, Stability},
pages = {659--676},
title = {On the stability of the Kerr metric},
volume = {221},
year = {2001}
}
@book{binney87,
address = {Princeton, NJ},
author = {Binney, J. and Tremaine, S.},
gbs_id = {01yNf7mipb0C},
keywords = {Stellar dynamics, Vlasov equation},
publisher = {Princeton University Press},
series = {Princeton Series in Astrophysics},
title = {Galactic Dynamics},
year = {1987}
}
@article{bizon00a,
adsurl = {http://adsabs.harvard.edu/abs/2000CMaPh.215...45B},
archiveprefix = {arXiv},
author = {Bizo{\'{n}}, P.},
doi = {10.1007/s002200000291},
eprint = {math-ph/9910026},
journal = {Commun. Math. Phys.},
keywords = {Critical collapse, Wave maps},
pages = {45--56},
title = {Equivariant Self-Similar Wave Maps from Minkowski Spacetime into 3-Sphere},
volume = {215},
year = {2000}
}
@article{bizon01a,
author = {Bizo{\'{n}}, P. and Chmaj, T. and Tabor, Z.},
doi = {10.1088/0951-7715/14/5/308},
eprint = {math-ph/0011005},
journal = {Nonlinearity},
keywords = {Critical collapse, Wave maps},
pages = {1041--1053},
title = {Formation of singularities for equivariant (2+1)-dimensional wave maps into the 2-sphere},
volume = {14},
year = {2001}
}
@article{bizon01b,
author = {Bizo{\'{n}}, P. and Tabor, Z.},
doi = {10.1103/PhysRevD.64.121701},
eid = {121701},
eprint = {math-ph/0105016},
journal = {Phys. Rev. D},
keywords = {Critical collapse, Wave maps},
pages = {1--4},
title = {On blowup for Yang--Mills fields},
volume = {64},
year = {2001}
}
@article{bizon02a,
author = {Bizo{\'{n}}, P. and Wasserman, A.},
cited = {5 February 2002},
doi = {10.1088/0264-9381/19/12/313},
eprint = {gr-qc/0201046},
journal = {Class. Quantum Grav.},
keywords = {Wave maps, Self-similarity, Critical collapse},
onlineversion = {http://arXiv.org/abs/gr-qc/0201046},
pages = {3309--3321},
title = {On the existence of self-similar spherically symmetric wave maps coupled to gravity},
volume = {19},
year = {2002}
}
@book{boerner93a,
address = {Berlin, Germany; New York, U.S.A.},
author = {B{\"{o}}rner, G.},
edition = {3rd},
keywords = {Cosmology},
publisher = {Springer},
series = {Texts and Monographs in Physics},
title = {The Early Universe: Facts and Fiction},
year = {1993}
}
@article{bourguignon92,
author = {Bourguignon, J.-P.},
journal = {Asterisque},
keywords = {Minkowski space, Nonlinear stability, Stability theory, Global existence},
pages = {321--358},
title = {Stabilit\'{e} par d\'{e}formation non-lin\'{e}aire de la m\'{e}trique de Minkowski (d'apr\`{e}s D. Christodoulou et S. Klainerman)},
volume = {201-203},
year = {1991}
}
@phdthesis{brauer95,
address = {Potsdam, Germany},
author = {Brauer, U.},
format = {phd},
keywords = {Euler equations, Singularities},
school = {Universit\"{a}t Potsdam},
title = {Singularit\"{a}ten in relativistischen Materiemodellen},
year = {1995}
}
@article{brauer94,
author = {Brauer, U. and Rendall, A. D. and Reula, O. A.},
doi = {10.1088/0264-9381/11/9/010},
eprint = {gr-qc/9403050},
journal = {Class. Quantum Grav.},
keywords = {Nonlinear stability, Stability theory, Global existence, No-hair theorems, Newtonian cosmology},
pages = {2283--2296},
title = {The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models},
volume = {11},
year = {1994}
}
@article{bressan95a,
author = {Bressan, A.},
doi = {10.1007/BF00392027},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Weak solutions, Global existence, Uniqueness theorems},
pages = {205--230},
title = {The Unique Limit of the Glimm Scheme},
volume = {130},
year = {1995}
}
@article{bressan95b,
author = {Bressan, A. and Colombo, R. M.},
doi = {10.1007/BF00375350},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Weak solutions, Global existence, Uniqueness theorems},
pages = {1--75},
title = {The Semigroup Generated by $2 \times 2$ Conservation Laws},
volume = {133},
year = {1995}
}
@book{bressan00a,
address = {Oxford, U.K.; New York, U.S.A.},
author = {Bressan, A.},
gbs_id = {ZVGGFWEprCYC},
keywords = {Hydrodynamics, Shocks, Weak solutions},
publisher = {Oxford University Press},
series = {Oxford Lecture Series in Mathematics and Its Applications},
title = {Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem},
volume = {20},
year = {2000}
}
@article{brodbeck97,
author = {Brodbeck, O. and Heusler, M. and Straumann, N. and Volkov, M.},
doi = {10.1103/PhysRevLett.79.4310},
eprint = {gr-qc/9707057},
journal = {Phys. Rev. Lett.},
keywords = {Einstein-Yang-Mills equations, Colored black holes},
pages = {4310--4313},
title = {Rotating solitons and non-rotating non-static black holes},
volume = {79},
year = {1997}
}
@article{burnett96,
author = {Burnett, G. A. and Rendall, A. D.},
doi = {10.1088/0264-9381/13/1/010},
journal = {Class. Quantum Grav.},
keywords = {Maximal hypersurfaces, Spherical symmetry},
pages = {111--123},
title = {Existence of maximal hypersurfaces in some spherically symmetric spacetimes},
volume = {13},
year = {1996}
}
@article{cantor79,
author = {Cantor, M.},
doi = {10.1063/1.524259},
journal = {J. Math. Phys.},
keywords = {Einstein constraints, Constraint equations, Asymptotically flat data},
pages = {1741--1744},
title = {A necessary and sufficient condition for York data to specify an asymptotically flat spacetime},
volume = {20},
year = {1979}
}
@article{carr00a,
author = {Carr, B. J. and Coley, A. A. and Goliath, M. and Nilsson, U. S. and Uggla, C.},
doi = {10.1103/PhysRevD.61.081502},
eid = {081502},
eprint = {gr-qc/9901031},
journal = {Phys. Rev. D},
keywords = {Self-similarity, Fluids, Critical collapse},
pages = {1--5},
title = {Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions},
volume = {61},
year = {2000}
}
@article{carr01a,
author = {Carr, B. J. and Coley, A. A. and Goliath, M. and Nilsson, U. S. and Uggla, C.},
doi = {10.1088/0264-9381/18/2/309},
journal = {Class. Quantum Grav.},
keywords = {Self-similarity, Fluids, Critical collapse},
pages = {303--324},
title = {The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models},
volume = {18},
year = {2001}
}
@book{cercignani88,
address = {Berlin, Germany; New York, U.S.A.},
author = {Cercignani, C.},
keywords = {Boltzmann equation},
publisher = {Springer},
series = {Applied Mathematical Sciences},
title = {The Boltzmann Equation and Its Applications},
volume = {67},
year = {1994}
}
@book{cercignani94,
address = {Berlin; New York},
author = {Cercignani, C. and Illner, R. and Pulvirenti, M.},
keywords = {Boltzmann equation},
publisher = {Springer},
series = {Applied Mathematical Sciences},
title = {The Mathematical Theory of Dilute Gases},
volume = {106},
year = {1988}
}
@article{chae01a,
author = {Chae, D.},
doi = {10.1088/0264-9381/18/21/313},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Scalar fields, Asymptotic flatness},
pages = {4589--4605},
title = {Global existence of spherically symmetric solutions to the coupled Einstein and nonlinear Klein--Gordon system.},
volume = {18},
year = {2001}
}
@article{chemin90,
author = {Chemin, J.-Y.},
doi = {10.1007/BF02097370},
journal = {Commun. Math. Phys.},
keywords = {Euler equations, Singularities},
pages = {323--339},
title = {Remarques sur l'apparition de singularit\'{e}s dans les \'{e}coulements Euleriens compressibles},
volume = {133},
year = {1990}
}
@article{chen95,
author = {Chen, J.},
doi = {10.1080/03605309508821145},
journal = {Commun. Part. Diff. Eq.},
keywords = {Euler equations, Weak solutions, Conservation laws},
pages = {1605--1646},
title = {Conservation laws for the relativistic $p$-system},
volume = {20},
year = {1995}
}
@article{chen97,
author = {Chen, J.},
doi = {10.1007/s002050050057},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Euler equations, Weak solutions, Conservation laws},
pages = {377--398},
title = {Conservation Laws for Relativistic Fluid Dynamics},
volume = {139},
year = {1997}
}
@article{choptuik93,
adsurl = {http://adsabs.harvard.edu/abs/1993PhRvL..70....9C},
author = {Choptuik, M. W.},
doi = {10.1103/PhysRevLett.70.9},
journal = {Phys. Rev. Lett.},
keywords = {Critical phenomena, Numerical relativity},
pages = {9--12},
title = {Universality and scaling in gravitational collapse of a massless scalar field},
volume = {70},
year = {1993}
}
@article{choquet69,
author = {Choquet-Bruhat, Y. and Geroch, R.},
doi = {10.1007/BF01645389},
journal = {Commun. Math. Phys.},
keywords = {Cauchy problem, Maximal development},
pages = {329--335},
title = {Global aspects of the Cauchy problem in general relativity},
volume = {14},
year = {1969}
}
@article{choquet00a,
author = {Choquet-Bruhat, Y. and Isenberg, J. A. and York Jr, J. W.},
eid = {084034},
journal = {Phys. Rev. D},
keywords = {Einstein constraints, Constraint equations},
pages = {1--20},
title = {Einstein constraints on asymptotically Euclidean manifolds},
volume = {61},
year = {2000}
}
@article{choquet01a,
author = {Choquet-Bruhat, Y. and Moncrief, V.},
doi = {10.1007/s00023-001-8602-5},
journal = {Ann. Henri Poincare},
keywords = {Einstein equations, Cosmology, Vacuum},
pages = {1007--1064},
title = {Future global in time Einsteinian spacetimes with U(1) isometry group},
volume = {2},
year = {2001}
}
@article{choquet02a,
author = {Choquet-Bruhat, Y. and Cotsakis, S.},
cited = {20 February 2002},
doi = {10.1016/S0393-0440(02)00028-1},
journal = {J. Geom. Phys.},
keywords = {Geodesic completeness},
pages = {345--350},
title = {Global hyperbolicity and completeness},
volume = {43},
year = {2002}
}
@incollection{choquet80,
address = {New York},
author = {Choquet-Bruhat, Y. and York, J. W.},
booktitle = {General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein},
editor = {Held, A.},
keywords = {Cauchy problem},
pages = {99--172},
publisher = {Plenum},
title = {The Cauchy problem},
volume = {1},
year = {1980}
}
@article{christodoulou86b,
author = {Christodoulou, D.},
doi = {10.1007/BF01463398},
journal = {Commun. Math. Phys.},
keywords = {Spherical symmetry, Scalar fields, Weak solutions},
pages = {587--621},
title = {Global existence of generalized solutions of the spherically symmetric Einstein-scalar equations in the large},
volume = {106},
year = {1986}
}
@article{christodoulou86a,
author = {Christodoulou, D.},
doi = {10.1007/BF01205930},
journal = {Commun. Math. Phys.},
keywords = {Spherical symmetry, Scalar fields},
pages = {337--361},
title = {The problem of a self-gravitating scalar field},
volume = {105},
year = {1986}
}
@article{christodoulou87b,
author = {Christodoulou, D.},
doi = {10.1007/BF01208960},
journal = {Commun. Math. Phys.},
keywords = {Spherical symmetry, Scalar fields, Gravitational collapse},
pages = {613--647},
title = {A mathematical theory of gravitational collapse},
volume = {109},
year = {1987}
}
@article{christodoulou87a,
author = {Christodoulou, D.},
doi = {10.1007/BF01208959},
journal = {Commun. Math. Phys.},
keywords = {Spherical symmetry, Scalar fields, Weak solutions},
pages = {591--611},
title = {The structure and uniqueness of generalised solutions of the spherically symmetric Einstein-scalar equations},
volume = {109},
year = {1987}
}
@article{christodoulou91,
author = {Christodoulou, D.},
doi = {10.1002/cpa.3160440305},
journal = {Commun. Pure Appl. Math.},
keywords = {Spherical symmetry, Scalar fields, Black holes, Singularities},
pages = {339--373},
title = {The formation of black holes and singularities in spherically symmetric gravitational collapse},
volume = {44},
year = {1991}
}
@article{christodoulou93a,
author = {Christodoulou, D.},
doi = {10.1002/cpa.3160460803},
journal = {Commun. Pure Appl. Math.},
keywords = {Spherical symmetry, Scalar fields, Functions of bounded variation},
pages = {1131--1220},
title = {Bounded Variation Solutions of the Spherically Symmetric Einstein-Scalar Field Equations},
volume = {46},
year = {1993}
}
@article{christodoulou94,
author = {Christodoulou, D.},
doi = {10.2307/2118619},
journal = {Ann. Math. (2)},
keywords = {Spherical symmetry, Scalar fields, Naked singularities, Self-similarity},
pages = {607--653},
title = {Examples of Naked Singularity Formation in the Gravitational Collapse of a Scalar Field},
volume = {140},
year = {1994}
}
@article{christodoulou95,
author = {Christodoulou, D.},
doi = {10.1007/BF00375144},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Euler equations, Shocks, Two-phase model},
pages = {343--400},
title = {Self-Gravitating Fluids: A Two-Phase Model},
volume = {130},
year = {1995}
}
@article{christodoulou96a,
author = {Christodoulou, D.},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Euler equations, Shocks, Two-phase model},
pages = {333--398},
title = {Self-Gravitating Fluids: The Continuation and Termination of a Free Phase Boundary},
volume = {133},
year = {1996}
}
@article{christodoulou96b,
author = {Christodoulou, D.},
doi = {10.1007/BF00379551},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Euler equations, Shocks, Two-phase model},
pages = {97--154},
title = {Self-Gravitating Fluids: The Formation of a Free Phase Boundary in the Phase Transition from Soft to Hard},
volume = {134},
year = {1996}
}
@article{christodoulou99,
author = {Christodoulou, D.},
doi = {10.2307/121023},
journal = {Ann. Math. (2)},
keywords = {Spherical symmetry, Scalar fields, Naked singularities, Nonlinear stability, Stability theory},
pages = {183--217},
title = {The instability of naked singularities in the gravitational collapse of a scalar field},
volume = {149},
year = {1999}
}
@article{christodoulou90,
author = {Christodoulou, D. and Klainerman, S.},
doi = {10.1002/cpa.3160430202},
journal = {Commun. Pure Appl. Math.},
keywords = {Minkowski space, Linear equations, Asymptotics},
pages = {137--199},
title = {Asymptotic properties of linear field equations in Minkowski space},
volume = {43},
year = {1990}
}
@book{christodoulou93b,
address = {Princeton, NJ},
author = {Christodoulou, D. and Klainerman, S.},
keywords = {Minkowski space, Nonlinear stability, Stability theory, Global existence},
publisher = {Princeton University Press},
series = {Princeton Mathematical Series},
title = {The Global Nonlinear Stability of the Minkowski Space},
volume = {41},
year = {1993}
}
@article{christodoulou81,
author = {Christodoulou, D. and {\'{O}} Murchadha, N.},
doi = {10.1007/BF01213014},
journal = {Commun. Math. Phys.},
keywords = {Einstein equations, Asymptotics},
pages = {271--300},
title = {The boost problem in general relativity},
volume = {80},
year = {1981}
}
@article{christodoulou00a,
author = {Christodoulou, D. and Lindblad, H.},
doi = {10.1002/1097-0312(200012)53:12<1536::AID-CPA2>3.0.CO;2-Q},
journal = {Commun. Pure Appl. Math.},
keywords = {Euler equations},
pages = {1536--1602},
title = {On the motion of the free surface of a liquid},
volume = {53},
year = {2000}
}
@article{zadeh93b,
author = {Christodoulou, D. and Tahvildar-Zadeh, A. S.},
doi = {10.1215/S0012-7094-93-07103-7},
journal = {Duke Math. J.},
keywords = {Wave maps, Asymptotics},
pages = {31--69},
title = {On the asymptotic behaviour of spherically symmetric wave maps},
volume = {71},
year = {1993}
}
@article{zadeh93a,
author = {Christodoulou, D. and Tahvildar-Zadeh, A. S.},
doi = {10.1002/cpa.3160460705},
journal = {Commun. Pure Appl. Math.},
keywords = {Wave maps, Global existence},
pages = {1041--1091},
title = {On the regularity of spherically symmetric wave maps},
volume = {46},
year = {1993}
}
@article{chrusciel90a,
author = {Chru{\'{s}}ciel, P. T.},
doi = {10.1016/0003-4916(90)90341-K},
journal = {Ann. Phys. (N.Y.)},
keywords = {Einstein equations, T2 symmetry, Cosmological spacetimes},
pages = {100--150},
title = {On Space-Times with $U(1)\times U(1)$ Symmetric Compact Cauchy Surfaces},
volume = {202},
year = {1990}
}
@book{chrusciel91a,
address = {Canberra},
author = {Chru{\'{s}}ciel, P. T.},
keywords = {Einstein equations, Global existence, Cosmic censorship},
publisher = {Australian National University Press},
series = {CMA Proceedings},
title = {On Uniqueness in the Large of Solutions of Einstein's Equations (Strong Cosmic Censorship)},
volume = {27},
year = {1991}
}
@article{Chrusciel91b,
author = {Chru{\'{s}}ciel, P. T.},
doi = {10.1007/BF02431882},
journal = {Commun. Math. Phys.},
keywords = {Einstein equations, Robinson-Trautman equation, Global existence},
pages = {289--313},
title = {Semi-global existence and convergence of solutions of the Robinson--Trautman (2-dimensional Calabi) equation},
volume = {137},
year = {1991}
}
@article{chrusciel90b,
author = {Chru{\'{s}}ciel, P. T. and Isenberg, J. and Moncrief, V.},
doi = {10.1088/0264-9381/7/10/003},
journal = {Class. Quantum Grav.},
keywords = {Cosmic censorship, Gowdy spacetime},
pages = {1671--1680},
title = {Strong Cosmic Censorship in Polarized Gowdy Spacetimes},
volume = {7},
year = {1990}
}
@article{claudel98,
author = {Claudel, C. M. and Newman, K. P.},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Cauchy problem, Hyperbolic equations, Singularities},
pages = {1073--1107},
title = {The Cauchy problem for quasi-linear hyperbolic evolution problems with a singularity in the time},
volume = {454},
year = {1998}
}
@article{coley92a,
author = {Coley, A. A. and Wainwright, J.},
journal = {Class. Quantum Grav.},
keywords = {Bianchi model, Fluids},
pages = {651--665},
title = {Qualitative analysis of two-fluid Bianchi cosmologies},
volume = {9},
year = {1992}
}
@article{corvino00a,
author = {Corvino, J.},
doi = {10.1007/PL00005533},
journal = {Commun. Math. Phys.},
keywords = {Einstein constraints},
pages = {137--189},
title = {Scalar curvature deformation and a gluing construction for the Einstein constraint equations},
volume = {214},
year = {2000}
}
@article{dain02a,
author = {Dain, S. and Nagy, G.},
cited = {30 January 2002},
eid = {084020},
journal = {Phys. Rev. D},
keywords = {Fluids, Constraints},
onlineversion = {http://arXiv.org/abs/gr-qc/0201091},
pages = {1--15},
title = {Initial data for fluid bodies in general relativity},
volume = {65},
year = {2002}
}
@article{damour02a,
author = {Damour, T. and Henneaux, M. and Rendall, A. D. and Weaver, M.},
cited = {20 February 2002},
doi = {10.1007/s000230200000},
eprint = {gr-qc/0202069},
journal = {Ann. Henri Poincare},
keywords = {Fuchsian equation, Singularities},
pages = {1049--1111},
title = {Kasner-like behaviour for subcritical Einstein-matter systems},
volume = {3},
year = {2002}
}
@article{diperna89,
author = {DiPerna, R. J. and Lions, P. L.},
doi = {10.2307/1971423},
journal = {Ann. Math.},
keywords = {Boltzmann equation, Global existence, Weak solutions},
pages = {321--366},
title = {On the Cauchy problem for Boltzmann equations: Global existence and weak stability},
volume = {130},
year = {1989}
}
@article{Dossa97,
author = {Dossa, M.},
journal = {Ann. Inst. Henri Poincare A},
keywords = {Characteristic initial value problem, Hyperbolic equations},
pages = {37--107},
title = {Espaces de Sobolev non isotropes, \`a poids et probl\`emes de Cauchy quasi-lin\'eaires sur un cono\"\i de caract\'eristique},
volume = {66},
year = {1997}
}
@article{dudynski92,
author = {Dudy{\'{n}}ski, M. and Ekiel-Je{\.{z}}ewska, M.},
doi = {10.1007/BF01055712},
journal = {J. Stat. Phys.},
keywords = {Boltzmann equation, Global existence},
pages = {991--1001},
title = {Global existence proof for the relativistic Boltzmann equation},
volume = {66},
year = {1992}
}
@article{eardley82,
author = {Eardley, D. M. and Moncrief, V.},
journal = {Commun. Math. Phys.},
keywords = {Yang-Mills equations, Global existence},
pages = {171--212},
title = {The global existence of Yang--Mills fields in $M^{3+1}$},
volume = {83},
year = {1982}
}
@inproceedings{ehlers91,
address = {Naples, Italy},
author = {Ehlers, J.},
booktitle = {Classical Mechanics and Relativity: Relationship and Consistency},
conference = {International Conference in Memory of Carlo Cattaneo, Elba 9--13 July 1989},
editor = {Ferrarese, G.},
keywords = {Newtonian limit},
publisher = {Bibliopolis},
series = {Monographs and Textbooks in Physical Science},
title = {The Newtonian limit of general relativity},
year = {1991}
}
@book{evans98,
address = {Providence, U.S.A.},
author = {Evans, L. C.},
gbs_id = {5Pv4LVB{\_}m8AC},
keywords = {Partial differential equations},
publisher = {American Mathematical Society},
series = {Graduate Studies in Mathematics},
title = {Partial Differential Equations},
volume = {19},
year = {1998}
}
@article{fischer99a,
author = {Fischer, A. and Moncrief, V.},
doi = {10.1088/0264-9381/16/11/102},
journal = {Class. Quantum Grav.},
keywords = {Cosmological models, Einstein equations},
pages = {L79--L87},
title = {The Einstein flow, the $\sigma$-constant and the geometriztion of 3-manifolds},
volume = {16},
year = {1999}
}
@article{friedrich86,
author = {Friedrich, H.},
doi = {10.1016/0393-0440(86)90004-5},
journal = {J. Geom. Phys.},
keywords = {Nonlinear stability, Stability theory, Global existence, No-hair theorems},
pages = {101--117},
title = {Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant},
volume = {3},
year = {1986}
}
@article{friedrich91,
author = {Friedrich, H.},
journal = {J. Differ. Geom.},
keywords = {Einstein-Yang-Mills equations, Global existence, Asymptotics},
pages = {275--345},
title = {On the global existence and asymptotic behaviour of solutions to the Einstein--Yang--Mills equations},
volume = {34},
year = {1991}
}
@article{friedrich95,
author = {Friedrich, H.},
doi = {10.1016/0393-0440(94)00042-3},
journal = {J. Geom. Phys.},
keywords = {Global existence, Asymptotics, Anti-de Sitter space},
pages = {125--184},
title = {Einstein equations and conformal structure: Existence of anti-de-Sitter-type space-times},
volume = {17},
year = {1995}
}
@article{friedrich96,
adsurl = {http://adsabs.harvard.edu/abs/1996CQGra..13.1451F},
author = {Friedrich, H.},
doi = {10.1088/0264-9381/13/6/014},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Hyperbolic equations, Reduction},
pages = {1451--1469},
title = {Hyperbolic reductions for Einstein's equations},
volume = {13},
year = {1996}
}
@article{friedrich98b,
author = {Friedrich, H.},
journal = {Phys. Rev. D},
keywords = {Euler equations, Lagrange coordinates},
pages = {2317--2322},
title = {Evolution equations for gravitating ideal fluid bodies in general relativity},
volume = {57},
year = {1998}
}
@article{friedrich98a,
author = {Friedrich, H.},
doi = {10.1016/S0393-0440(97)82168-7},
journal = {J. Geom. Phys.},
keywords = {Einstein equations, Global existence, Asymptotics},
pages = {83--163},
title = {Gravitational fields near space-like and null infinity},
volume = {24},
year = {1998}
}
@article{friedrich99a,
adsurl = {http://adsabs.harvard.edu/abs/1999CMaPh.201..619F},
author = {Friedrich, H. and Nagy, G.},
doi = {10.1007/s002200050571},
journal = {Commun. Math. Phys.},
keywords = {Einstein equations, Initial boundary value problem},
pages = {619--655},
title = {The Initial Boundary Value Problem for Einstein's Vacuum Field Equation},
volume = {201},
year = {1999}
}
@incollection{friedrich00a,
address = {Berlin; New York},
archiveprefix = {arXiv},
author = {Friedrich, H. and Rendall, A. D.},
booktitle = {Einstein's Field Equations and Their Physical Implications: Selected Essays in Honour of J\"{u}rgen Ehlers},
editor = {Schmidt, B. G.},
eprint = {gr-qc/0002074},
gbs_id = {vjjAvE{\_}iXnkC{\&}pg=PA127},
keywords = {Einstein equations, Cauchy problem},
pages = {127--223},
publisher = {Springer},
series = {Lecture Notes in Physics},
title = {The Cauchy Problem for the Einstein Equations},
volume = {540},
year = {2000}
}
@article{fritelli94,
author = {Frittelli, S. and Reula, O. A.},
doi = {10.1007/BF02112314},
journal = {Commun. Math. Phys.},
keywords = {Einstein equations, Newtonian limit},
pages = {221--235},
title = {On the Newtonian Limit of General Relativity},
volume = {166},
year = {1994}
}
@article{glassey97,
author = {Glassey, R. T. and Schaeffer, J.},
doi = {10.1007/s002200050090},
journal = {Commun. Math. Phys.},
keywords = {Vlasov-Maxwell system, Global existence},
pages = {257--284},
title = {The `Two and One--Half Dimensional' Relativistic Vlasov--Maxwell System},
volume = {185},
year = {1997}
}
@article{glassey98a,
author = {Glassey, R. T. and Schaeffer, J.},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Vlasov-Maxwell system, Global existence},
pages = {331--354},
title = {The Relativistic Vlasov--Maxwell System in Two Space Dimensions: Part I},
volume = {141},
year = {1998}
}
@article{glassey98b,
author = {Glassey, R. T. and Schaeffer, J.},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Vlasov-Maxwell system, Global existence},
pages = {355--374},
title = {The Relativistic Vlasov--Maxwell System in Two Space Dimensions: Part II},
volume = {141},
year = {1998}
}
@article{glassey93,
author = {Glassey, R. T. and Strauss, W.},
doi = {10.2977/prims/1195167275},
journal = {Publ. Res. Inst. Math. Sci.},
keywords = {Boltzmann equation, Global existence, Stability, Stability theory},
pages = {301--347},
title = {Asymptotic stability of the relativistic Maxwellian},
volume = {29},
year = {1993}
}
@article{glimm65,
author = {Glimm, J.},
doi = {10.1002/cpa.3160180408},
journal = {Commun. Pure Appl. Math.},
keywords = {Global existence, Weak solutions},
pages = {697--715},
title = {Solutions in the large for nonlinear hyperbolic systems of equations},
volume = {18},
year = {1965}
}
@article{goliath98a,
author = {Goliath, M. and Nilsson, U. S. and Uggla, C.},
journal = {Class. Quantum Grav.},
keywords = {Critical phenomena, Self-similarity},
pages = {167--186},
title = {Spatially self-similar spherically symmetric perfect-fluid models},
volume = {15},
year = {1998}
}
@article{goliath98b,
author = {Goliath, M. and Nilsson, U. S. and Uggla, C.},
journal = {Class. Quantum Grav.},
keywords = {Critical phenomena, Self-similarity},
pages = {2841--2863},
title = {Timelike self-similar spherically symmetric perfect-fluid models},
volume = {15},
year = {1998}
}
@article{grassin98,
author = {Grassin, M.},
doi = {10.1512/iumj.1998.47.1608},
journal = {Indiana Univ. Math. J.},
keywords = {Euler equations, Global existence},
pages = {1397--1432},
title = {Global smooth solutions to Euler equations for a perfect gas},
volume = {47},
year = {1998}
}
@article{gundlach98,
author = {Gundlach, C.},
eprint = {gr-qc/9712084},
journal = {Adv. Theor. Math. Phys.},
keywords = {Critical phenomena},
pages = {1--49},
title = {Critical phenomena in gravitational collapse},
volume = {2},
year = {1998}
}
@article{gundlach99,
author = {Gundlach, C.},
cited = {22 December 1999},
eid = {lrr-1999-4},
journal = {Living Rev. Relativity},
keywords = {Critical phenomena},
title = {Critical Phenomena in Gravitational Collapse},
url = {http://www.livingreviews.org/lrr-1999-4},
volume = {2},
year = {1999}
}
@article{guo95a,
author = {Guo, Y. and Strauss, W.},
journal = {Ann. Inst. Henri Poincare C},
keywords = {Instability, Plasma physics, Kinetic theory},
pages = {339--352},
title = {Nonlinear instability of double-humped equilibria},
volume = {12},
year = {1995}
}
@article{guo98a,
author = {Guo, Y.},
doi = {10.1007/s002200050388},
journal = {Commun. Math. Phys.},
keywords = {Euler equations, Global existence},
pages = {249--265},
title = {Smooth irrotational flows in the large to the Euler--Poisson system},
volume = {195},
year = {1998}
}
@article{guo01a,
author = {Guo, Y. and Rein, G.},
doi = {10.1007/s002200100434},
journal = {Commun. Math. Phys.},
keywords = {Vlasov equation, Stability, Stability theory},
pages = {607--629},
title = {Isotropic steady states in stellar dynamics},
volume = {219},
year = {2001}
}
@inproceedings{guo99a,
address = {Providence, U.S.A.},
author = {Guo, Y. and Tahvildar-Zadeh, A. S.},
booktitle = {Nonlinear Partial Differential Equations},
conference = {International Conference on Nonlinear Partial Differential Equations and Applications, March 21--24, 1998, Northwestern University},
editor = {Chen, G.-Q. and DiBenedetto, E.},
keywords = {Euler equations, Singularities},
publisher = {American Mathematical Society},
series = {Contemporary Mathematics},
title = {Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics},
volume = {238},
year = {1999}
}
@book{hartman82,
address = {Boston, U.S.A.},
author = {Hartman, P.},
edition = {2nd},
keywords = {Ordinary differential equations},
publisher = {Birkh\"{a}user},
title = {Ordinary Differential Equations},
year = {1982}
}
@article{halliwell87,
author = {Halliwell, J. J.},
doi = {10.1016/0370-2693(87)91011-2},
journal = {Phys. Lett. B},
keywords = {Inflation, Scalar fields},
pages = {341--344},
title = {Scalar fields in cosmology with an exponential potential},
volume = {185},
year = {1987}
}
@article{hamilton82a,
author = {Hamilton, R.},
journal = {J. Differ. Geom.},
keywords = {Curvature, Ricci flow},
pages = {255--306},
title = {Three manifolds of positive Ricci curvature},
volume = {17},
year = {1982}
}
@article{hauser01,
author = {Hauser, I. and Ernst, F. J.},
journal = {Gen. Relativ. Gravit.},
keywords = {Existence theorems, Einstein equations},
pages = {195--293},
title = {Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation},
volume = {33},
year = {2001}
}
@article{heilig95,
author = {Heilig, U.},
doi = {10.1007/BF02099884},
journal = {Commun. Math. Phys.},
keywords = {Einstein equations, Newtonian limit},
pages = {457--493},
title = {On the existence of rotating stars in general relativity},
volume = {166},
year = {1995}
}
@article{henkel01a,
author = {Henkel, O.},
cited = {28 January 2002},
doi = {10.1017/S0305004102006515},
journal = {Math. Proc. Camb. Phil. Soc.},
keywords = {Cosmology, Foliations},
pages = {551--571},
title = {Local prescribed mean curvature foliations in cosmological spacetimes},
volume = {134},
year = {2003}
}
@article{henkel01b,
author = {Henkel, O.},
cited = {28 January 2002},
doi = {10.1063/1.1466882},
journal = {J. Math. Phys.},
keywords = {Cosmology, Foliations},
onlineversion = {http://arXiv.org/abs/gr-qc/0110081},
pages = {2439--2465},
title = {Global prescribed mean curvature foliations in cosmological space-times. I},
volume = {43},
year = {2002}
}
@article{henkel01c,
author = {Henkel, O.},
cited = {28 January 2002},
doi = {10.1063/1.1466883},
journal = {J. Math. Phys.},
keywords = {Cosmology, Foliations},
onlineversion = {http://arXiv.org/abs/gr-qc/0110082},
pages = {2466--2485},
title = {Global prescribed mean curvature foliations in cosmological space-times. II},
volume = {43},
year = {2002}
}
@article{heusler98,
author = {Heusler, M.},
cited = {12 December 1999},
eid = {lrr-1998-6},
journal = {Living Rev. Relativity},
keywords = {Black holes, Stationary solutions},
title = {Stationary Black Holes: Uniqueness and Beyond},
url = {http://www.livingreviews.org/lrr-1998-6},
volume = {1},
year = {1998}
}
@book{heusler96,
address = {Cambridge; New York},
author = {Heusler, M.},
gbs_id = {l62FvO{\_}qRe8C},
keywords = {Black holes, No-hair theorems},
publisher = {Cambridge University Press},
title = {Black Hole Uniqueness Theorems},
year = {1996}
}
@article{hewitt01,
author = {Hewitt, C. and Wainwright, J.},
doi = {10.1023/A:1002075902953},
journal = {Gen. Relativ. Gravit.},
keywords = {Bianchi model},
pages = {65--94},
title = {The asymptotic regimes of tilted Bianchi II cosmologies},
volume = {33},
year = {2001}
}
@book{hubbard91,
address = {Berlin},
author = {Hubbard, J. H. and West, B. H.},
edition = {3rd},
keywords = {Dynamical systems, Ordinary differential equations},
publisher = {Springer},
series = {Texts in Applied Mathematics},
title = {Differential Equations: A Dynamical Systems Approach. Ordinary Differential Equations},
volume = {5},
year = {1991}
}
@article{isenberg95,
author = {Isenberg, J. A.},
doi = {10.1088/0264-9381/12/9/013},
journal = {Class. Quantum Grav.},
keywords = {Einstein constraints, Constraint equations, Existence theorems},
pages = {2249--2274},
title = {Constant mean curvature solutions of the Einstein constraint equations on closed manifolds},
volume = {12},
year = {1995}
}
@article{isenberg99a,
author = {Isenberg, J. and Kichenassamy, S.},
doi = {10.1063/1.532775},
journal = {J. Math. Phys.},
keywords = {Fuchsian equation, Singularities},
pages = {340--352},
title = {Asymptotic behavior in polarized $T^{2}$-symmetric vacuum space-times},
volume = {40},
year = {1999}
}
@article{isenberg90,
author = {Isenberg, J. and Moncrief, V.},
doi = {10.1016/0003-4916(90)90369-Y},
journal = {Ann. Phys. (N.Y.)},
keywords = {Gowdy spacetime, Cosmic censorship},
pages = {84--122},
title = {Asymptotic behavior of the gravitational field and the nature of singularities in Gowdy spacetimes},
volume = {199},
year = {1990}
}
@article{isenberg96,
author = {Isenberg, J. A. and Moncrief, V.},
doi = {10.1088/0264-9381/13/7/015},
journal = {Class. Quantum Grav.},
keywords = {Einstein constraints, Constraint equations, Existence theorems},
pages = {1819--1847},
title = {A set of nonconstant mean curvature solutions of the Einstein constraint equations on closed manifolds},
volume = {13},
year = {1996}
}
@article{isenberg98,
author = {Isenberg, J. A. and Rendall, A. D.},
doi = {10.1088/0264-9381/15/11/025},
journal = {Class. Quantum Grav.},
keywords = {Constant mean curvature hypersurfaces, Dust},
pages = {3679--3688},
title = {Cosmological spacetimes not covered by a constant mean curvature slicing},
volume = {15},
year = {1998}
}
@article{jensen87,
author = {Jensen, L. G. and Stein-Schabes, J. A.},
journal = {Phys. Rev. D},
keywords = {Inflation},
pages = {1146--1150},
title = {Is inflation natural?},
volume = {35},
year = {1987}
}
@book{john82,
address = {Berlin; New York},
author = {John, F.},
edition = {4th},
keywords = {Partial differential equations},
publisher = {Springer},
series = {Applied Mathematical Sciences},
title = {Partial Differential Equations},
volume = {1},
year = {1982}
}
@book{john90,
address = {Providence, RI},
author = {John, F.},
gbs_id = {wx0Bq5oCTasC},
keywords = {Hyperbolic equations, Singularities},
publisher = {American Mathematical Society},
series = {University Lecture Series},
title = {Nonlinear Wave Equations, Formation of Singularities},
volume = {2},
year = {1990}
}
@article{kichenassamy96c,
author = {Kichenassamy, S.},
doi = {10.1080/03605309608821177},
journal = {Commun. Part. Diff. Eq.},
keywords = {Fuchsian equation, Singularities, Nash-Moser theorem},
pages = {125--162},
title = {The blow-up problem for exponential nonlinearities},
volume = {21},
year = {1996}
}
@article{kichenassamy96b,
author = {Kichenassamy, S.},
doi = {10.1006/jdeq.1996.0033},
journal = {J. Differ. Equations},
keywords = {Fuchsian equation, Singularities},
pages = {299--327},
title = {Fuchsian equations in Sobolev spaces and blow-up},
volume = {125},
year = {1996}
}
@book{kichenassamy96a,
address = {New York},
author = {Kichenassamy, S.},
gbs_id = {yARyD5cuaiUC},
keywords = {Hyperbolic equations},
publisher = {Marcel Dekker},
series = {Monographs and Textbooks in Pure and Applied Mathematics},
title = {Nonlinear Wave Equations},
volume = {194},
year = {1996}
}
@article{kichenassamy93a,
author = {Kichenassamy, S. and Littman, W.},
journal = {Commun. Part. Diff. Eq.},
keywords = {Fuchsian equation, Singularities},
pages = {431--452},
title = {Blow-up surfaces for nonlinear wave equations, I},
volume = {18},
year = {1993}
}
@article{kichenassamy93b,
author = {Kichenassamy, S. and Littman, W.},
journal = {Commun. Part. Diff. Eq.},
keywords = {Fuchsian equation, Singularities},
pages = {1869--1899},
title = {Blow-up surfaces for nonlinear wave equations, II},
volume = {18},
year = {1993}
}
@article{kichenassamy98a,
author = {Kichenassamy, S. and Rendall, A. D.},
doi = {10.1088/0264-9381/15/5/016},
journal = {Class. Quantum Grav.},
keywords = {Fuchsian equation, Singularities, Gowdy spacetime},
pages = {1339--1355},
title = {Analytic description of singularities in Gowdy spacetimes},
volume = {15},
year = {1998}
}
@article{kind93,
author = {Kind, S. and Ehlers, J.},
journal = {Class. Quantum Grav.},
keywords = {Euler equations, Free boundary, Local existence},
pages = {2123--2136},
title = {Initial boundary value problem for the spherically symmetric Einstein equations for a perfect fluid},
volume = {18},
year = {1993}
}
@article{kitada92,
author = {Kitada, Y. and Maeda, K.},
journal = {Phys. Rev. D},
keywords = {Inflation, Scalar fields},
pages = {1416--1419},
title = {Cosmic no-hair theorem in power-law inflation},
volume = {45},
year = {1992}
}
@article{kitada93,
author = {Kitada, Y. and Maeda, K.},
doi = {10.1088/0264-9381/10/4/008},
journal = {Class. Quantum Grav.},
keywords = {Inflation, Scalar fields},
pages = {703--734},
title = {Cosmic no-hair theorem in homogeneous cosmological models. I. Bianchi models.},
volume = {10},
year = {1993}
}
@article{klainerman95,
author = {Klainerman, S. and Machedon, M.},
doi = {10.2307/2118611},
journal = {Ann. Math.},
keywords = {Yang-Mills equations, Global existence},
pages = {39--119},
title = {Finite energy solutions of the Yang--Mills equations in ${\bf R}^{3+1}$},
volume = {142},
year = {1995}
}
@article{klainerman01a,
author = {Klainerman, S.},
journal = {Int. Math. Res. Notices},
keywords = {Einstein equations, Global existence},
number = {5},
pages = {221--274},
title = {A commuting vector fields approach to Strichartz-type inequalities and applications to quasi-linear wave equations},
volume = {2001},
year = {2001}
}
@preprint{klainerman01b,
author = {Klainerman, S. and Rodnianski, I.},
cited = {1 March 2002},
eid = {math.AP/0109173},
format = {arxiv},
keywords = {Existence theorems, Einstein equations},
month = {September},
title = {Rough solution for the Einstein vacuum equations},
url = {http://arXiv.org/abs/math.AP/0109173},
year = {2001}
}
@article{klainerman99,
author = {Klainerman, S. and Nicol{\`{o}}, F.},
doi = {10.1088/0264-9381/16/8/201},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Global existence},
pages = {R73--R157},
title = {On local and global aspects of the Cauchy problem in general relativity},
volume = {16},
year = {1999}
}
@article{kleihaus98,
author = {Kleihaus, B. and Kunz, J.},
doi = {10.1103/PhysRevD.57.834},
eprint = {gr-qc/9707045},
journal = {Phys. Rev. D},
keywords = {Einstein-Yang-Mills equations},
pages = {834--856},
title = {Static axially symmetric Einstein-Yang-Mills-Dilaton solutions: Regular solutions},
volume = {57},
year = {1998}
}
@article{kunze01a,
author = {Kunze, M. and Rendall, A. D.},
doi = {10.1007/s00023-001-8596-z},
journal = {Ann. Henri Poincare},
keywords = {Vlasov equation, Radiation damping},
pages = {857--886},
title = {The Vlasov--Poisson system with radiation damping},
volume = {2},
year = {2001}
}
@article{kunze01b,
author = {Kunze, M. and Rendall, A. D.},
doi = {10.1088/0264-9381/18/17/311},
journal = {Class. Quantum Grav.},
keywords = {Vlasov equation, Radiation damping},
pages = {3573--3587},
title = {Simplified models of electromagnetic and gravitational radiation damping.},
volume = {18},
year = {2001}
}
@article{leblanc95a,
author = {LeBlanc, V. G. and Kerr, D. and Wainwright, J.},
doi = {10.1088/0264-9381/12/2/020},
journal = {Class. Quantum Grav.},
keywords = {Bianchi model, Electromagnetic fields},
pages = {513--541},
title = {Asymptotic states of magnetic Bianchi VI${}_0$ cosmologies},
volume = {12},
year = {1995}
}
@article{leblanc97a,
author = {LeBlanc, V. G.},
doi = {10.1088/0264-9381/14/8/025},
journal = {Class. Quantum Grav.},
keywords = {Bianchi model, Electromagnetic fields},
pages = {2281--2301},
title = {Asymptotic states of magnetic Bianchi I cosmologies},
volume = {14},
year = {1997}
}
@article{leblanc98a,
author = {LeBlanc, V. G.},
doi = {10.1088/0264-9381/15/6/016},
journal = {Class. Quantum Grav.},
keywords = {Bianchi model, Electromagnetic fields},
pages = {1607--1626},
title = {Bianchi II magnetic cosmologies},
volume = {15},
year = {1998}
}
@article{lifshitz63,
author = {Lifshitz, E. M. and Khalatnikov, I. M.},
doi = {10.1080/00018736300101283},
journal = {Adv. Phys.},
keywords = {Singularities},
pages = {185--249},
title = {Investigations in relativistic cosmology},
volume = {12},
year = {1963}
}
@article{lin90a,
author = {Lin, X. F. and Wald, R. M.},
journal = {Phys. Rev. D},
keywords = {Bianchi model, Maximal hypersurfaces},
pages = {2444--2448},
title = {Proof of the closed universe recollapse conjecture for general Bianchi type IX cosmologies},
volume = {41},
year = {1990}
}
@article{lin97,
author = {Lin, S. S.},
doi = {10.1137/S0036141095292883},
journal = {SIAM J. Math. Anal.},
keywords = {Euler equations, Spherical symmetry, Stars, Stability, Stability theory},
pages = {539--569},
title = {Stability of gaseous stars in spherically symmetric motions},
volume = {28},
year = {1997}
}
@article{lindblom94,
author = {Lindblom, L. and Masood-ul-Alam, A. K. M.},
doi = {10.1007/BF02105189},
journal = {Commun. Math. Phys.},
keywords = {Euler equations, Spherical symmetry, Stars},
pages = {123--145},
title = {On the spherical symmetry of static stellar models},
volume = {162},
year = {1994}
}
@article{lions94,
author = {Lions, P. L.},
journal = {J. Math. Kyoto Univ.},
keywords = {Boltzmann equation},
pages = {391--427},
title = {Compactness in Boltzmann's equation via Fourier integral operators and applications. I},
volume = {34},
year = {1994}
}
@article{lions91,
author = {Lions, P. L. and Perthame, B.},
doi = {10.1007/BF01232273},
journal = {Invent. Math.},
keywords = {Vlasov equation, Global existence},
pages = {415--430},
title = {Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system},
volume = {105},
year = {1991}
}
@book{longair98a,
address = {Berlin, Germany; New York, U.S.A.},
author = {Longair, M. S.},
gbs_id = {2ARuLT-tk5EC},
keywords = {Galaxies},
publisher = {Springer},
series = {Astronomy and Astrophysics Library},
title = {Galaxy Formation},
year = {1998}
}
@book{majda84,
address = {Berlin, Germany; New York, U.S.A.},
author = {Majda, A.},
gbs_id = {3ItbIwkt0eMC},
keywords = {Hyperbolic equations, Hydrodynamics},
publisher = {Springer},
series = {Applied Mathematical Sciences},
title = {Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables},
volume = {53},
year = {1984}
}
@article{makino98,
author = {Makino, T.},
journal = {J. Math. Kyoto Univ.},
keywords = {Euler equations, Stars},
pages = {55--69},
title = {On spherically symmetric stellar models in general relativity},
volume = {38},
year = {1998}
}
@article{makino00a,
author = {Makino, T.},
journal = {Funkcialaj Ekvacioj},
keywords = {Euler equations, Stars},
pages = {471--489},
title = {On the spiral structure of the (R,M) diagram for a stellar model of the Tolman--Oppenheimer--Volkoff equation},
volume = {43},
year = {2000}
}
@article{martingarcia01,
author = {Mart{\'{\i}}n-Garc{\'{\i}}a, J. M. and Gundlach, C.},
cited = {17 January 2002},
doi = {10.1103/PhysRevD.65.084026},
eid = {084026},
eprint = {gr-qc/0112009},
journal = {Phys. Rev. D},
keywords = {General relativity, Vlasov equation, Gravitation},
onlineversion = {http://arXiv.org/abs/gr-qc/0112009},
pages = {1--18},
title = {Self-similar spherically symmetric solutions of the massless Einstein--Vlasov system},
volume = {65},
year = {2002}
}
@article{misner67a,
author = {Misner, C. W.},
doi = {10.1103/PhysRevLett.22.1071},
journal = {Phys. Rev. Lett.},
keywords = {Mixmaster},
pages = {1071--1074},
title = {Mixmaster Universe},
volume = {22},
year = {1969}
}
@article{moncrief81b,
author = {Moncrief, V.},
doi = {10.1016/0003-4916(81)90270-0},
journal = {Ann. Phys. (N.Y.)},
keywords = {Gowdy spacetime, Global existence},
pages = {87--107},
title = {Global Properties of Gowdy Spacetimes with $T^{3} \times R$ Topology},
volume = {132},
year = {1981}
}
@article{moncrief82,
author = {Moncrief, V.},
doi = {10.1016/0003-4916(82)90273-1},
journal = {Ann. Phys. (N.Y.)},
keywords = {Cauchy horizons},
pages = {83--103},
title = {Neighbourhoods of Cauchy horizons in cosmological spacetimes with one Killing field},
volume = {141},
year = {1982}
}
@article{moncrief81a,
author = {Moncrief, V. and Eardley, D. M.},
doi = {10.1007/BF00764275},
journal = {Gen. Relativ. Gravit.},
keywords = {Cosmic censorship, Global existence},
pages = {887--892},
title = {The Global Existence Problem and Cosmic Censorship in General Relativity},
volume = {13},
year = {1981}
}
@article{moss86,
author = {Moss, I. and Sahni, V.},
doi = {10.1016/0370-2693(86)91488-7},
journal = {Phys. Lett. B},
keywords = {Inflation, Scalar fields},
pages = {159--162},
title = {Anisotropy in the chaotic inflationary universe},
volume = {178},
year = {1986}
}
@article{mucha99,
author = {Mucha, P. B.},
doi = {10.1007/s002200050607},
journal = {Commun. Math. Phys.},
keywords = {Boltzmann equation, Global existence},
pages = {107--118},
title = {Global existence for the Einstein--Boltzmann equation in flat Robertson--Walker spacetime},
volume = {203},
year = {1999}
}
@article{newman93a,
author = {Newman, R. P. A. C.},
journal = {Proc. R. Soc. London},
keywords = {Einstein equations, Singularities},
pages = {473--492},
title = {On the Structure of Conformal Singularities in Classical General Relativity},
volume = {443},
year = {1993}
}
@article{newman93b,
author = {Newman, R. P. A. C.},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Einstein equations, Singularities},
pages = {493--515},
title = {On the structure of conformal singularities in classical general relativity. II Evolution equations and a conjecture of K. P. Tod},
volume = {443},
year = {1993}
}
@article{nilsson00a,
author = {Nilsson, U. S. and Hancock, M. J. and Wainwright, J.},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Dynamical systems},
pages = {3119--3134},
title = {Non-tilted Bianchi VII${}_0$ models -- the radiation fluid.},
volume = {17},
year = {2000}
}
@article{olabarrieta02a,
author = {Olabarrieta, I. and Choptuik, M. W.},
doi = {10.1103/PhysRevD.65.024007},
eid = {024007},
eprint = {gr-qc/0107076},
journal = {Phys. Rev. D},
keywords = {Critical collapse, Collisionless matter},
pages = {1--10},
title = {Critical phenomena at the threshold of black hole formation for collisionless matter in spherical symmetry},
volume = {65},
year = {2001}
}
@article{oliveira02a,
author = {de Oliveira, H. P. and Ozorio de Almeida, A. M. and Dami{\~{a}}o Soares, I. and Tonini, E. V.},
cited = {17 February 2002},
eid = {083511},
journal = {Phys. Rev. D},
keywords = {Bianchi model, Inflation},
onlineversion = {http://arXiv.org/abs/gr-qc/0202047},
pages = {1--9},
title = {Homoclinic chaos in the dynamics of a general Bianchi type-IX model},
volume = {65},
year = {2002}
}
@article{park00,
author = {Park, J.},
doi = {10.1023/A:1001875224949},
journal = {Gen. Relativ. Gravit.},
keywords = {Spherical symmetry, Elasticity},
pages = {235--252},
title = {Static solutions of the Einstein equations for spherically symmetric elastic bodies},
volume = {32},
year = {2000}
}
@article{pfaffelmoser92,
author = {Pfaffelmoser, K.},
doi = {10.1016/0022-0396(92)90033-J},
journal = {J. Differ. Equations},
keywords = {Vlasov equation, Global existence},
pages = {281--303},
title = {Global classical solutions of the Vlasov--Poisson system in three dimensions for general initial data},
volume = {95},
year = {1992}
}
@book{racke92,
address = {Wiesbaden, Germany},
author = {Racke, R.},
keywords = {Hyperbolic equations},
publisher = {Vieweg},
series = {Aspects of Mathematics},
title = {Lectures on Nonlinear Evolution Equations: Initial Value Problems},
volume = {19},
year = {1992}
}
@article{rein00a,
author = {Rein, G.},
doi = {10.1016/S0362-546X(98)00280-6},
journal = {Nonlinear Anal.},
keywords = {Spherical symmetry, Vlasov equation, Stellar dynamics},
pages = {313--344},
title = {Stationary and static stellar dynamical models with axial symmetry},
volume = {41},
year = {2000}
}
@article{rein90,
author = {Rein, G.},
doi = {10.1007/BF02097656},
journal = {Commun. Math. Phys.},
keywords = {Vlasov equation, Maxwell theory, Global existence},
pages = {41--78},
title = {Generic global solutions of the relativistic Vlasov--Maxwell system of plasma physics},
volume = {135},
year = {1990}
}
@article{rein94a,
author = {Rein, G.},
doi = {10.1017/S0305004100072303},
journal = {Math. Proc. Camb. Phil. Soc.},
keywords = {Vlasov equation, Stellar dynamics},
pages = {559--570},
title = {Static solutions of the spherically symmetric Vlasov--Einstein system},
volume = {115},
year = {1994}
}
@article{rein96a,
author = {Rein, G.},
doi = {10.1017/S0305004100074569},
journal = {Math. Proc. Camb. Phil. Soc.},
keywords = {Einstein-Vlasov system, Singularities, Cosmological spacetimes, Spherical symmetry},
pages = {739--762},
title = {Cosmological solutions of the Vlasov--Einstein system with spherical, plane and hyperbolic symmetry},
volume = {119},
year = {1996}
}
@article{rein97,
author = {Rein, G.},
doi = {10.1007/s002050050070},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Nonlinear stability, Stability theory, Newtonian cosmology},
pages = {335--351},
title = {Nonlinear Stability of Homogeneous Models in Newtonian Cosmology},
volume = {140},
year = {1997}
}
@article{rein98a,
author = {Rein, G. and Rendall, A. D.},
doi = {10.1017/S0305004199004193},
journal = {Math. Proc. Camb. Phil. Soc.},
keywords = {Vlasov equation, Stellar dynamics},
pages = {363--380},
title = {Compact support of spherically symmetric equilibria in relativistic and non-relativistic galactic dynamics},
volume = {128},
year = {2000}
}
@article{rein92,
author = {Rein, G. and Rendall, A. D.},
doi = {10.1007/BF02096962},
journal = {Commun. Math. Phys.},
keywords = {Vlasov equation, Stellar dynamics, Global existence},
pages = {561--583},
title = {Global existence of solutions of the spherically symmetric Vlasov--Einstein system with small initial data},
volume = {150},
year = {1992}
}
@article{rein93,
author = {Rein, G. and Rendall, A. D.},
journal = {Ann. Inst. Henri Poincare A},
keywords = {Vlasov equation, Stellar dynamics},
pages = {383--397},
title = {Smooth static solutions of the spherically symmetric Vlasov--Einstein system},
volume = {59},
year = {1993}
}
@article{rein94b,
author = {Rein, G. and Rendall, A. D.},
doi = {10.1007/BF00391558},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Global existence, Newtonian cosmology},
pages = {183--201},
title = {Global Existence of Classical Solutions to the Vlasov--Poisson System in a Three Dimensional, Cosmological Setting},
volume = {126},
year = {1994}
}
@article{rein95a,
author = {Rein, G. and Rendall, A. D. and Schaeffer, J.},
doi = {10.1007/BF02101839},
journal = {Commun. Math. Phys.},
keywords = {Vlasov equation, Global existence, Spherical symmetry},
pages = {467--478},
title = {A regularity theorem for solutions of the spherically symmetric Vlasov--Einstein system},
volume = {168},
year = {1995}
}
@article{rein99a,
author = {Rein, G.},
doi = {10.1512/iumj.1999.48.1636},
journal = {Indiana Univ. Math. J.},
keywords = {Vlasov equation, Stellar dynamics},
pages = {335--346},
title = {Static shells for the Vlasov--Poisson and Vlasov--Einstein systems},
volume = {48},
year = {1999}
}
@article{rein98b,
author = {Rein, G. and Rendall, A. D. and Schaeffer, J.},
doi = {10.1103/PhysRevD.58.044007},
eid = {044007},
eprint = {gr-qc/9804040},
journal = {Phys. Rev. D},
keywords = {Vlasov equation, Critical phenomena, Numerical relativity},
pages = {1--8},
title = {Critical collapse of collisionless matter: A numerical investigation},
volume = {58},
year = {1998}
}
@article{rendall90,
author = {Rendall, A. D.},
doi = {10.1098/rspa.1990.0009},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Characteristic initial value problem},
pages = {221--239},
title = {Reduction of the Characteristic Initial Value Problem to the Cauchy Problem and Its Applications to the Einstein Equations},
volume = {427},
year = {1990}
}
@article{rendall92b,
author = {Rendall, A. D.},
doi = {10.1063/1.529766},
journal = {J. Math. Phys.},
keywords = {Euler equations, Local existence},
pages = {1047--1053},
title = {The initial value problem for a class of general relativistic fluid bodies},
volume = {33},
year = {1992}
}
@article{rendall92a,
author = {Rendall, A. D.},
doi = {10.1098/rspa.1992.0111},
journal = {Proc. R. Soc. London, Ser. A},
keywords = {Post-Newtonian approximations, Newtonian limit},
pages = {341--360},
title = {On the definition of post-Newtonian approximations},
volume = {438},
year = {1992}
}
@article{rendall94a,
author = {Rendall, A. D.},
doi = {10.1007/BF02101736},
eprint = {gr-qc/9303027},
journal = {Commun. Math. Phys.},
keywords = {Newtonian limit, Einstein-Vlasov system},
pages = {89--112},
title = {The Newtonian limit for asymptotically flat solutions of the Einstein-Vlasov system},
volume = {163},
year = {1994}
}
@article{rendall94b,
author = {Rendall, A. D.},
doi = {10.1006/aphy.1994.1061},
journal = {Ann. Phys. (N.Y.)},
keywords = {Cosmic censorship, Bianchi model, Einstein-Vlasov system},
pages = {82--96},
title = {Cosmic censorship for some spatially homogeneous cosmological models},
volume = {233},
year = {1994}
}
@article{rendall95a,
author = {Rendall, A. D.},
doi = {10.1088/0264-9381/12/6/017},
journal = {Class. Quantum Grav.},
keywords = {Constant mean curvature hypersurfaces, Cosmological spacetimes, Spherical symmetry},
pages = {1517--1533},
title = {Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry},
volume = {12},
year = {1995}
}
@article{rendall95b,
author = {Rendall, A. D.},
doi = {10.1007/BF02107959},
journal = {Gen. Relativ. Gravit.},
keywords = {Scalar fields, Plane symmetry, Singularities},
pages = {213--221},
title = {On the nature of singularities in plane symmetric scalar field cosmologies.},
volume = {27},
year = {1995}
}
@article{rendall95c,
author = {Rendall, A. D.},
doi = {10.1017/S0305004100073837},
journal = {Math. Proc. Camb. Phil. Soc.},
keywords = {Bianchi model, Singularities},
pages = {511--526},
title = {Global properties of locally spatially homogeneous cosmological models with matter},
volume = {118},
year = {1995}
}
@article{rendall96a,
author = {Rendall, A. D.},
eprint = {gr-qc/9606049},
journal = {Helv. Phys. Acta},
keywords = {Constant mean curvature hypersurfaces, Cosmological spacetimes},
pages = {490--500},
title = {Constant mean curvature foliations in cosmological spacetimes},
volume = {69},
year = {1996}
}
@article{rendall96b,
author = {Rendall, A. D.},
doi = {10.1063/1.531400},
journal = {J. Math. Phys.},
keywords = {Bianchi model, Cosmological spacetimes, Singularities},
pages = {438--451},
title = {The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I.},
volume = {37},
year = {1996}
}
@article{rendall97a,
author = {Rendall, A. D.},
doi = {10.1016/S0362-546X(96)00203-9},
journal = {Nonlinear Anal.},
keywords = {Constant mean curvature hypersurfaces, Cosmological spacetimes},
pages = {3589--3598},
title = {Existence and non-existence results for global constant mean curvature foliations},
volume = {30},
year = {1997}
}
@article{rendall97b,
author = {Rendall, A. D.},
doi = {10.1007/s002200050194},
journal = {Commun. Math. Phys.},
keywords = {Constant mean curvature hypersurfaces, Cosmological spacetimes, T2 symmetry},
pages = {145--164},
title = {Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry},
volume = {189},
year = {1997}
}
@article{rendall97d,
author = {Rendall, A. D.},
doi = {10.1088/0264-9381/14/8/028},
eprint = {gr-qc/9703036},
journal = {Class. Quantum Grav.},
keywords = {Mixmaster, Dynamical systems, Cosmological spacetimes},
pages = {2341--2356},
title = {Global dynamics of the mixmaster model},
volume = {14},
year = {1997}
}
@inproceedings{rendall97e,
address = {Warsaw},
author = {Rendall, A. D.},
booktitle = {Mathematics of Gravitation, Part I: Lorentzian Geometry and Einstein Equations},
conference = {Proceedings of the Workshop on Mathematical Aspects of Theories of Gravitation, held in Warsaw, February 29\,--\,March 30, 1996},
editor = {Chru{\'{s}}ciel, P. T.},
keywords = {Vlasov equation, Global existence, Spherical symmetry},
pages = {35--68},
publisher = {Polish Academy of Sciences, Institute of Mathematics},
series = {Banach Center Publications},
title = {An introduction to the Einstein--Vlasov system},
volume = {41},
year = {1997}
}
@inproceedings{rendall97c,
address = {Singapore; River Edge, NJ},
author = {Rendall, A. D.},
booktitle = {General Relativity and Gravitation},
conference = {Proceedings of the 14th International Conference on General Relativity and Gravitation, Florence, Italy, 6\,--\,12 August 1995},
editor = {Francaviglia, M. and Longhi, G. and Lusanna, L. and Sorace, E.},
eprint = {gr-qc/9510009},
keywords = {Einstein equations, Existence theorems},
pages = {313--335},
publisher = {World Scientific},
title = {Solutions of the Einstein equations with matter},
year = {1997}
}
@article{rendall91,
author = {Rendall, A. D. and Schmidt, B. G.},
doi = {10.1088/0264-9381/8/5/022},
journal = {Class. Quantum Grav.},
keywords = {Euler equations, Stars},
pages = {985--1000},
title = {Existence and properties of spherically symmetric static fluid bodies with given equation of state},
volume = {8},
year = {1991}
}
@article{rendall99a,
author = {Rendall, A. D. and Tod, K. P.},
doi = {10.1088/0264-9381/16/6/305},
journal = {Class. Quantum Grav.},
keywords = {Vlasov equation, Bianchi model, Dynamical systems},
pages = {1705--1726},
title = {Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric},
volume = {16},
year = {1999}
}
@article{rendall00a,
author = {Rendall, A. D. and Uggla, C.},
doi = {10.1088/0264-9381/17/22/310},
journal = {Class. Quantum Grav.},
keywords = {Vlasov equation, Bianchi model, Dynamical systems},
pages = {4697--4713},
title = {Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations},
volume = {17},
year = {2000}
}
@article{rendall00b,
author = {Rendall, A. D.},
doi = {10.1088/0264-9381/17/16/313},
eprint = {gr-qc/0004044},
journal = {Class. Quantum Grav.},
keywords = {Fuchsian equation, Gowdy models},
pages = {3305--3316},
title = {Fuchsian analysis of singularities in Gowdy spacetimes beyond analyticity},
volume = {17},
year = {2000}
}
@inproceedings{rendall00c,
address = {Nantes, France},
author = {Rendall, A. D.},
booktitle = {Proceedings of Journ\'{e}es Equations aux D\'{e}riv\'{e}es Partielles},
cited = {1 March 2002},
conference = {La Chapelle sur Erdre, Nantes, France, 5-9 June 2000},
editor = {Depauw, N. and Robert, D. and Saint-Raymond, X.},
keywords = {Einstein equations, Existence theorems},
onlineversion = {http://www.numdam.org/item?id=JEDP_2000____A14_0},
pages = {XIV-1--12},
publisher = {University of Nantes},
title = {Blow-up for solutions of hyperbolic PDE and spacetime singularities},
year = {2000}
}
@article{rendall01a,
author = {Rendall, A. D. and Weaver, M.},
doi = {10.1088/0264-9381/18/15/310},
eprint = {gr-qc/0103102},
journal = {Class. Quantum Grav.},
keywords = {Gowdy equations, Spikes},
pages = {2959--2975},
title = {Manufacture of Gowdy spacetimes with spikes},
volume = {18},
year = {2001}
}
@article{rendall01b,
author = {Rendall, A. D.},
cited = {21 January 2002},
doi = {10.1023/A:1019734703162},
journal = {Gen. Relativ. Gravit.},
keywords = {Center manifolds, Cosmological models, Inflation},
onlineversion = {http://arXiv.org/abs/gr-qc/0112040},
pages = {1277--1294},
title = {Cosmological Models and Centre Manifold Theory},
volume = {34},
year = {2002}
}
@article{ringstrom00a,
author = {Ringstr{\"{o}}m, H.},
doi = {10.1088/0264-9381/17/4/301},
eprint = {gr-qc/9911115},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Singularities, Cosmology},
pages = {713--731},
title = {Curvature blow up in Bianchi VIII and IX vacuum spacetimes},
volume = {4},
year = {2000}
}
@article{ringstrom00b,
author = {Ringstr{\"{o}}m, H.},
doi = {10.1007/PL00001041},
eprint = {gr-qc/0006035},
journal = {Ann. Henri Poincare},
keywords = {Einstein equations, Singularities, Cosmology},
pages = {405--500},
title = {The Bianchi IX attractor},
volume = {2},
year = {2001}
}
@article{ringstrom01a,
author = {Ringstr{\"{o}}m, H.},
doi = {10.1088/0264-9381/18/18/302},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Bianchi model, Cosmology},
pages = {3791--3824},
title = {The future asymptotics of Bianchi VIII vacuum solutions},
volume = {18},
year = {2001}
}
@article{schaeffer99,
author = {Schaeffer, J.},
doi = {10.1007/s002200050647},
journal = {Commun. Math. Phys.},
keywords = {Vlasov equation, Stellar dynamics},
pages = {313--327},
title = {A class of counterexamples to Jeans' theorem for the Vlasov--Einstein system},
volume = {204},
year = {1999}
}
@article{secchi91,
author = {Secchi, P.},
journal = {Ann. Scuola Norm. Sup. Pisa},
keywords = {Fluids, Free boundary},
pages = {295--318},
title = {On the equations of viscous gaseous stars},
volume = {18},
year = {1991}
}
@article{shapiro85,
author = {Shapiro, S. L. and Teukolsky, S. A.},
doi = {10.1086/163588},
journal = {Astrophys. J.},
keywords = {Vlasov equation, Stellar dynamics, Numerical relativity},
pages = {58--79},
title = {Relativistic stellar dynamics on the computer: II. Physical applications},
volume = {298},
year = {1985}
}
@article{sideris79,
author = {Sideris, T.},
journal = {Commun. Math. Phys.},
keywords = {Euler equations, Singularities, Shock waves},
pages = {475--485},
title = {Formation of singularities in three-dimensional compressible fluids},
volume = {101},
year = {1979}
}
@article{smoller93,
author = {Smoller, J. A. and Temple, B.},
journal = {Commun. Math. Phys.},
keywords = {Euler equations, Weak solutions, Global existence},
pages = {65--100},
title = {Global solutions of the relativistic Euler equations},
volume = {156},
year = {1993}
}
@article{smoller91,
adsurl = {http://adsabs.harvard.edu/abs/1991CMaPh.143..115S},
author = {Smoller, J. A. and Wasserman, A. G. and Yau, S.-T. and McLeod, J. B.},
doi = {10.1007/BF02100288},
journal = {Commun. Math. Phys.},
keywords = {Bartnik-McKinnon solutions, Existence theorems},
pages = {115--147},
title = {Smooth static solutions of the Einstein/Yang-Mills equations},
volume = {143},
year = {1991}
}
@article{stahl01a,
author = {St{\aa}hl, F.},
cited = {31 January 2002},
doi = {10.1088/0264-9381/19/17/301},
eprint = {gr-qc/0109011},
journal = {Class. Quantum Grav.},
keywords = {Gowdy spacetime, Fuchsian equation},
onlineversion = {http://arXiv.org/abs/gr-qc/0109011},
pages = {4483--4504},
title = {Fuchsian analysis of $\mathbf{S}^{2} \times \mathbf{S}^{1}$ and $\mathbf{S}^{3}$ Gowdy spacetimes},
volume = {19},
year = {2002}
}
@book{strauss89,
address = {Providence, U.S.A.},
author = {Strauss, W.},
gbs_id = {CLGGJXyah14C},
keywords = {Hyperbolic equations},
publisher = {American Mathematical Society},
series = {Regional Conference Series in Mathematics},
title = {Nonlinear Wave Equations},
volume = {73},
year = {1989}
}
@online{struwepreprints,
author = {Struwe, M.},
cited = {17 January 2002},
format = {personal homepage},
keywords = {Existence theorems, Wave maps, Singularities},
month = {January},
publisher = {ETH Zurich},
title = {Publications of Michael Struwe},
url = {http://www.math.ethz.ch/~struwe/CV/publications.html},
year = {2002}
}
@book{taylor91,
address = {Boston, U.S.A.},
author = {Taylor, M. E.},
gbs_id = {B9k7QRzXCO4C},
keywords = {Pseudodifferential operators, Partial differential equations},
publisher = {Birkh\"{a}user},
series = {Progress in Mathematics},
title = {Pseudodifferential Operators and Nonlinear PDE},
volume = {100},
year = {1991}
}
@book{taylor96,
address = {Berlin, Germany; New York, U.S.A.},
author = {Taylor, M. E.},
gbs_id = {uphqFYqYm0oC},
keywords = {Partial differential equations},
publisher = {Springer},
series = {Applied Mathematical Sciences},
title = {Partial Differential Equations},
volume = {115-117},
year = {1996}
}
@book{thurston97a,
address = {Princeton, U.S.A.},
author = {Thurston, W.},
keywords = {Geometrization},
publisher = {Princeton University Press},
series = {Princeton Mathematical Series},
title = {Three-dimensional geometry and topology, Vol. 1},
volume = {35},
year = {1997}
}
@article{goode85,
author = {Goode, S. W. and Wainwright, J.},
doi = {10.1088/0264-9381/2/1/010},
journal = {Class. Quantum Grav.},
keywords = {Einstein equations, Singularities},
pages = {99--115},
title = {Isotropic singularities in cosmological models},
volume = {2},
year = {1985}
}
@book{wainwright97,
address = {Cambridge; New York},
author = {Wainwright, J. and Ellis, G. F. R.},
gbs_id = {7W9WpW8zP6oC},
keywords = {Dynamical systems, Cosmological spacetimes},
publisher = {Cambridge University Press},
title = {Dynamical Systems in Cosmology},
year = {1997}
}
@article{wainwright99a,
author = {Wainwright, J. and Hancock, M. J. and Uggla, C.},
doi = {10.1088/0264-9381/16/8/302},
journal = {Class. Quantum Grav.},
keywords = {Bianchi model},
pages = {2577--2598},
title = {Asymptotic self-similarity breaking at late times in cosmology},
volume = {16},
year = {1999}
}
@article{wald83,
author = {Wald, R. M.},
journal = {Phys. Rev. D},
keywords = {Inflation, Cosmological constant},
pages = {2118--2120},
title = {Asymptotic behaviour of homogeneous cosmological models with cosmological constant},
volume = {28},
year = {1983}
}
@article{weaver99a,
author = {Weaver, M.},
doi = {10.1088/0264-9381/17/2/311},
eprint = {gr-qc/9909043},
journal = {Class. Quantum Grav.},
keywords = {Cosmology, Magnetic fields, Dynamical systems, Mixmaster},
pages = {421--434},
title = {Dynamics of magnetic Bianchi VI${}_0$ cosmologies},
volume = {17},
year = {2000}
}
@article{witt86,
author = {Witt, D.},
doi = {10.1103/PhysRevLett.57.1386},
journal = {Phys. Rev. Lett.},
keywords = {Einstein constraints, Constraint equations},
pages = {1386--1389},
title = {Vacuum spacetimes that admit no maximal slice},
volume = {57},
year = {1986}
}
@article{wolansky01a,
author = {Wolansky, G.},
doi = {10.1007/s002050000122},
journal = {Arch. Ration. Mech. Anal.},
keywords = {Stability, Vlasov equation},
pages = {205--230},
title = {Static Solutions of the Vlasov--Einstein System},
volume = {156},
year = {2001}
}
@inproceedings{woodhouse97,
address = {Warsaw, Poland},
author = {Woodhouse, N. M. J.},
booktitle = {Mathematics of Gravitation, Part I: Lorentzian Geometry and Einstein Equations},
conference = {Proceedings of the Workshop on Mathematical Aspects of Theories of Gravitation, held in Warsaw, Poland, February 29 -- March 30, 1996},
editor = {Chru{\'{s}}ciel, P. T.},
keywords = {Twistors, Global existence},
pages = {221--232},
publisher = {Polish Academy of Sciences, Institute of Mathematics},
series = {Banach Center Publications},
title = {Integrability and Einstein's equations},
volume = {41},
year = {1997}
}
@article{wu99,
author = {Wu, S.},
doi = {10.1090/S0894-0347-99-00290-8},
journal = {J. Amer. Math. Soc.},
keywords = {Euler equations, Local existence},
pages = {445--495},
title = {Well-posedness in Sobolev spaces of the full water wave problem in 3-D},
volume = {12},
year = {1999}
}
@article{york99,
author = {York Jr, J. W.},
doi = {10.1103/PhysRevLett.82.1350},
journal = {Phys. Rev. Lett.},
keywords = {Constraint equations},
pages = {1350--1353},
title = {Conformal `Thin-Sandwich' Data for the Initial-Value Problem of General Relativity},
volume = {82},
year = {1999}
}