Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-06-16
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, Latex, report # 3
Scientific paper
10.1007/BF00391558
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.
Rein Gerhard
Rendall Alan D.
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