Isotropic Steady States in Galactic Dynamics

The present paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov--Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of isotropic, spherically symmetric steady states and prove their nonlinear stability against {general}, i. e., not necessarily symmetric perturbations. The class is optimal in a certain sense, in particular, it includes all polytropes of finite mass with decreasing dependence on the particle energy.

Authors and Affiliations

1. Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University,¶Providence, RI 02912, USA, , , , , , US

   Yan Guo

2. Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany, , , , , , DE

   Gerhard Rein

Received: 24 October 2000 / Accepted: 7 January 2001

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