Non-linear stability of gaseous stars

TL;DR

This paper demonstrates the non-linear stability of gaseous star models by constructing steady states as energy minimizers within the Euler-Poisson framework, extending stability results using an energy-Casimir approach.

Contribution

It introduces a novel stability proof for gaseous star models via energy minimization, linking Euler-Poisson steady states to Vlasov-Poisson stability results.

Findings

Steady states are constructed as energy minimizers.

These states are proven non-linearly stable against general perturbations.

The approach extends previous Vlasov-Poisson stability results.

Abstract

We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general, i.e., not necessarily spherically symmetric perturbations. The mathematical approach is based on previous stability results for the Vlasov-Poisson system by Y. Guo and the author, exploiting the energy-Casimir technique. The analysis is conditional in the sense that it assumes the existence of solutions to the initial value problem for the Euler-Poisson system which preserve mass and energy. The relation between the Euler-Poisson and the Vlasov-Poisson system in this context is also explored.