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

TL;DR

This paper proves the existence and stability of static shell solutions in a spherically symmetric Vlasov-Poisson system with a central point mass, modeling a galaxy around a black hole, using variational methods.

Contribution

It establishes global existence of classical solutions with shell-like initial data and demonstrates the existence and stability of static shell solutions via a variational approach.

Findings

Global existence of classical solutions for shell-like initial data

Existence of stable static shell solutions

Application of variational methods to stability analysis

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.