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Archive for Rational Mechanics and Analysis

, Volume 194, Issue 3, pp 743–773 | Cite as

Asymptotic Behavior and Orbital Stability of Galactic Dynamics in Relativistic Scalar Gravity

  • Simone CalogeroEmail author
  • Óscar Sánchez
  • Juan Soler
Article

Abstract

The Nordström–Vlasov system is a relativistic Lorentz invariant generalization of the Vlasov–Poisson system in the gravitational case. The asymptotic behavior of solutions and the non-linear stability of steady states are investigated. It is shown that solutions of the Nordström–Vlasov system with energy greater or equal to the mass satisfy a dispersion estimate in terms of the conformal energy. When the energy is smaller than the mass, we prove the existence and non-linear (orbital) stability of a class of static solutions (isotropic polytropes) against general perturbations. The proof of orbital stability is based on a variational problem associated to the minimization of the energy functional under suitable constraints.

Keywords

Nonlinear Stability Orbital Stability Conformal Energy Virial Theorem Dispersion Estimate 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Departamento de Matemática AplicadaFacultad de Ciencias, Universidad de GranadaGranadaSpain

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