Skip to main content
SpringerLink
Log in

Flat Steady States in Stellar Dynamics – Existence and Stability

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

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

    Gerhard Rein

Authors
  1. Gerhard Rein
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 26 October 1998 / Accepted: 23 February 1999

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rein, G. Flat Steady States in Stellar Dynamics – Existence and Stability. Commun. Math. Phys. 205, 229–247 (1999). https://doi.org/10.1007/s002200050674

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002200050674

Search

Navigation