Inventiones mathematicae

, Volume 187, Issue 1, pp 145–194 | Cite as

Orbital stability of spherical galactic models

  • Mohammed Lemou
  • Florian Méhats
  • Pierre Raphaël


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.


Weak Solution Spherical Model Nonlinear Stability Orbital Stability Anisotropic Model 
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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Mohammed Lemou
    • 1
  • Florian Méhats
    • 2
  • Pierre Raphaël
    • 3
  1. 1.CNRS and IRMARUniversité de Rennes 1RennesFrance
  2. 2.IRMARUniversité de Rennes 1RennesFrance
  3. 3.IMTUniversité Paul SabatierToulouseFrance

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