Stable steady states in stellar dynamics

TL;DR

This paper proves the existence and nonlinear stability of certain steady states in stellar dynamics modeled by the Vlasov-Poisson system, extending known classes of solutions and their stability properties.

Contribution

It introduces a new method for establishing the stability of a broader class of steady states in stellar dynamics.

Findings

Existence of stable steady states in the Vlasov-Poisson system.

Extension of stability results to new classes of polytropic states.

Application of energy-Casimir functional minimization for stability analysis.

Abstract

We prove the existence and nonlinear stability of steady states of the Vlasov-Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy-Casimir functional from which fact their dynamical stability is deduced. The analysis applies to some of the well-known polytropic steady states, but it also considerably extends the class of known steady states.