Three global existence theorems have been proved in Newtonian
cosmology. The first [46] is an analogue of the cosmic no hair theorem (cf. Section
5.1) and concerns models with a positive cosmological constant. It
asserts that homogeneous and isotropic models are nonlinearly
stable if the matter is described by dust or a polytropic fluid
with pressure. Thus, it gives information about global existence
and asymptotic behaviour for models arising from small (but
finite) perturbations of homogeneous and isotropic data. The
second and third results concern collisionless matter and the
case of vanishing cosmological constant. The second [196] says that data that constitute a periodic (but not necessarily
small) perturbation of a homogeneous and isotropic model that
expands indefinitely give rise to solutions that exist globally
in the future. The third [191] says that the homogeneous and isotropic models in Newtonian
cosmology that correspond to a
*k*
=-1 Friedmann-Robertson-Walker model in general relativity are
non-linearly stable.

Theorems on Existence and Global Dynamics for the
Einstein Equations
Alan D. Rendall
http://www.livingreviews.org/lrr-2002-6
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