Orbital stability of spherical galactic models

• 成果类型: Article
• 署名作者: Lemou, Mohammed; Mehats, Florian; Raphael, Pierre
• 署名单位: Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0332-9
• 发表日期: 2012
• 页码: 145-194
• 关键词: vlasov-poisson system; concentration-compactness principle; self-gravitating system; phase-space density; nonlinear stability; ground-states; steady-states; singularity formation; energy; calculus

摘要

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 (Binney, Tremaine in Galactic Dynamics, Princeton University Press, Princeton, 1987) 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 (Sov. Astron. 4:859-867, 1961). In the previous work (Lemou et al. in A new variational approach to the stability of gravitational systems, submitted, 2011), we derived the stability of anisotropic models under spherically symmetric perturbations using fundamental monotonicity properties of the Hamiltonian under suitable generalized symmetric rearrangements first observed in the physics literature (Lynden-Bell in Mon. Not. R. Astron. Soc. 144:189-217, 1969; Gardner in Phys. Fluids 6:839-840, 1963; Wiechen et al. in Mon. Not. R. Astron. Soc. 223:623-646, 1988; Aly in Mon. Not. R. Astron. Soc. 241:15, 1989). In this work, we show how this approach combined with a new generalized Antonov type coercivity property implies the orbital stability of spherical models under general perturbations.