Orbital stability of spherical galactic models

TL;DR

This paper proves the orbital stability of spherical galactic models in the gravitational Vlasov-Poisson system under general perturbations, extending previous linear and symmetric stability results using a new coercivity approach.

Contribution

It introduces a novel generalized Antonov coercivity property that, combined with previous methods, establishes orbital stability under broad perturbations.

Findings

Orbital stability of spherical models is proven.

New coercivity property is developed.

Stability results extend beyond symmetric perturbations.

Abstract

We consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture is the stability of spherical models which are nonincreasing radially symmetric steady states solutions. This conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by Antonov in 1961. In a previous work (arXiv:0904.2443), we derived the stability of anisotropic models under {\it spherically symmetric perturbations} using fundamental monotonicity properties of the Hamiltonian under suitable generalized symmetric rearrangements first observed in the physics litterature. In this work, we show how this approach combined with a {\it new generalized} Antonov type coercivity property implies the orbital stability of spherical models under general perturbations.