Archive for Rational Mechanics and Analysis

, Volume 171, Issue 3, pp 301–327 | Cite as

Asymptotic Behaviour for the Vlasov-Poisson System in the Stellar-Dynamics Case

  • Jean DolbeaultEmail author
  • Óscar Sánchez
  • Juan Soler


We study an optimal inequality which relates potential and kinetic energies in an appropriate framework for bounded solutions of the Vlasov-Poisson (VP) system. Optimal distribution functions, which are completely characterized, minimize the total energy. From this variational approach, we deduce bounds for the kinetic and potential energies in terms of conserved quantities (mass and total energy) of the solutions of the VP system and a nonlinear stability result. Then we apply our estimates to the study of the large-time asymptotics and observe two different regimes.


Distribution Function Kinetic Energy Total Energy Potential Energy Asymptotic Behaviour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Ceremade (UMR CNRS no. 7534)Université Paris IX-DauphineParis Cédex 16France
  2. 2.Departamento de Matemática AplicadaFacultad de ciencias, Universidad de GranadaSpain

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