Orbital stability of spherical galactic models

Mohammed Lemou (1) , Florian Méhats (2, 1) , Pierre Raphaël (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IPSO - Invariant Preserving SOlvers
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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, 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.

Mots clés: VLASOV-POISSON SYSTEM; CONCENTRATION-COMPACTNESS PRINCIPLE; SELF-GRAVITATING SYSTEM; PHASE SPACE DENSITY; NONLINEAR STABILITY; STELLAR-DYNAMICS; GROUND-STATES; STEADY-STATES; SINGULARITY FORMATION; POLYTROPIC GALAXIES

Domaines: Equations aux dérivées partielles [math.AP]

Mohammed Lemou, Florian Méhats, Pierre Raphaël. Orbital stability of spherical galactic models. Inventiones Mathematicae, 2012, 187 (1), pp.145-194. ⟨10.1007/s00222-011-0332-9⟩. ⟨hal-00505327⟩