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Existence and stability of static shells for the Vlasov–Poisson system with a fixed central point mass

Published online by Cambridge University Press:  01 March 2009

ACHIM SCHULZE
ACHIM SCHULZE*
Affiliation:
Mathematisches Institut der Universität Bayreuth D 95440 Bayreuth, Germany. e-mail: achim.schulze@yahoo.de
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Abstract

We consider the Vlasov–Poisson system with spherical symmetry and an exterior potential which is induced by a point mass in the center. This system can be used as a simple model for a newtonian galaxy surrounding a black hole. For this system, we establish a global existence result for classical solutions with shell-like initial data, i.e. the support of the density is bounded away from the point mass singularity. We also prove existence and stability of stationary solutions which describe static shells, where we use a variational approach which was established by Y. Guo and G. Rein.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 489 - 511
Copyright
Copyright © Cambridge Philosophical Society 2008

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