Stability of spherically symmetric steady states in galactic dynamics against general perturbations

TL;DR

This paper demonstrates the nonlinear stability of spherically symmetric steady states in galactic dynamics under general perturbations, extending previous results that were limited to symmetric perturbations.

Contribution

It introduces a method to prove the nonlinear stability of these steady states against arbitrary perturbations, removing the previous symmetry restriction.

Findings

Nonlinear stability holds against general perturbations

Extension of stability results beyond symmetric cases

Method applicable to Vlasov-Poisson system

Abstract

Certain steady states of the Vlasov-Poisson system can be characterized as minimizers of an energy-Casimir functional, and this fact implies a nonlinear stability property of such steady states. In previous investigations by Y. Guo and the author stability was obtained only with respect to spherically symmetric perturbations. In the present investigation we show how to remove this unphysical restriction.