Orbital stability for the gravitational Vlasov-Poisson system, after Lemou-Méhats-Raphaël, Guo, Lin, Rein et al.

Stabilité orbitale pour le système de Vlasov-Poisson gravitationnel, d'après Lemou-Méhats-Raphaël, Guo, Lin, Rein et al.

Clément Mouhot (1)

1 DPMMS - Department of Pure Mathematics and Mathematical Statistics

This paper reviews the recent mathematical progresses made on the study of the orbital stability properties for the gravitational Vlasov-Poisson system. We present in details the paper of Lemou, Méhats and Raphaël (Inventiones 2011) and we review also the previous works by Dolbeault, Guo, Hadzic, Lin, Rein, Sánchez, Soler, Wan, Wolansky. We also include a discussion of the history of this topic and the pioneering works by physicists like Antonov, Lynden-Bell and Aly. This is the text of a Bourbaki seminar given in november 2011

Mots clés: Vlasov-Poisson; stabilité orbitale; orbital stability; galaxy models; problème variationnel; variational problem; inégalité de réarrangement; rearrangement inequality

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Clément Mouhot. Stabilité orbitale pour le système de Vlasov-Poisson gravitationnel, d'après Lemou-Méhats-Raphaël, Guo, Lin, Rein et al.. 2013. ⟨hal-00658222v2⟩