Flat steady states in stellar dynamics - existence and stability

TL;DR

This paper proves the existence and stability of flat, steady-state solutions in a simplified 2D model of stellar dynamics, relevant for modeling flattened galaxies, and provides examples of partially singular solutions.

Contribution

It establishes the existence and stability of flat steady states in a 2D Vlasov-Poisson system, a novel mathematical result for astrophysical models.

Findings

Existence of steady states as energy-Casimir minimizers

Dynamical stability of these states

Examples of partially singular solutions

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 partially singular solutions of the three dimensional Vlasov-Poisson system.