Three global existence theorems have been proved in Newtonian cosmology. The first is an analogue of the cosmic no hair theorem (cf. Section 4.1) 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 says that data which constitute a periodic (but not necessarily small) perturbation of a homogeneous and isotropic model which expands indefinitely give rise to solutions which exist globally in the future. The third says that the homogeneous and isotropic models in Newtonian cosmology which correspond to a k =-1 Friedmann-Robertson-Walker model in general relativity are non-linearly stable.
|Local and global existence theorems for the Einstein
Alan D. Rendall
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