Arch. Rational Mech. Anal. 126, 183 - 201 (1994)
Global existence of classical solutions to the Vlasov-Poisson
system in a three-dimensional, cosmological setting
G. Rein, A. D. Rendall¹
1) Max-Planck-Institut für Gravitationsphysik,
Schlaatzweg 1, 14479 Potsdam, Germany
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.
Gerhard Rein (rein@rz.mathematik.uni-muenchen.de)