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Communications in Mathematical Physics

, Volume 205, Issue 1, pp 229–247 | Cite as

Flat Steady States in Stellar Dynamics – Existence and Stability

  • Gerhard Rein
Article

Abstract:

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 singular solutions of the three dimensional Vlasov–Poisson system.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Gerhard Rein
    • 1
  1. 1.Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany.¶E-mail: rein@rz.mathematik.uni-muenchen.deGermany

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