Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

TL;DR

This paper proves the global existence and uniqueness of classical solutions to a modified Vlasov-Poisson system in a three-dimensional cosmological setting, specifically for spatially periodic deviations from homogeneous states.

Contribution

It extends the understanding of the Vlasov-Poisson system to cosmological models with non-zero homogeneous backgrounds, providing new existence results.

Findings

Global existence and uniqueness of solutions established.

Solutions for spatially periodic deviations are well-posed.

The work applies to Newtonian cosmological models with homogeneous backgrounds.

Abstract

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.