Flat steady states in stellar dynamics - existence and stability

Details Flat steady states in stellar dynamics - existence and stability Flat steady states in stellar dynamics - existence and stability

1998-10-22

arxiv.org/abs/math-ph/9810013v1

Commun. Math. Phys. 205, 229-247 (1999)

Physics

Mathematical Physics

25 pages, LaTeX

Scientific paper

10.1007/s002200050674

We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a mathematics point of view these steady states provide examples of partially singular solutions of the three dimensional Vlasov-Poisson system.

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