Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : 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.
 
 
ASYMPTOTIC BEHAVIOUR FOR THE VLASOV-POISSON SYSTEM IN THE STELLAR DYNAMIC CASE
DOLBEAULT Jean, SANCHEZ Oscar, SOLER Juan
2003-7
24-02-2003
 
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
Téléphone : +33 (0)1 44-05-49-23 - fax : +33 (0)1 44-05-45-99