A constraint variational problem arising in stellar dynamics

TL;DR

This paper analyzes a variational problem related to the stability of steady states in stellar dynamics using compactness results, providing a new proof within a general framework for such problems.

Contribution

It introduces a novel proof approach for a variational problem in stellar dynamics, expanding the theoretical framework for stability analysis of the Vlasov-Poisson system.

Findings

Established a new proof for the variational problem

Connected the problem to a general framework by Guo and Rein

Enhanced understanding of stability criteria in stellar models

Abstract

We use the compactness result of A. Burchard and Y. Guo (cf. \cite{BuGu}) to analyze the reduced 'energy' functional arising naturally in the stability analysis of steady states of the Vlasov-Poisson system (cf. \cite{SaSo} and \cite{Ha}). We consider the associated variational problem and present a new proof that puts it in the general framework for tackling the variational problems of this type, given by Y. Guo and G. Rein (cf. \cite{Re1} and \cite{Re2}).