Asymptotic Behaviour for the Vlasov-Poisson System in the Stellar-Dynamics Case
Dolbeault, Jean; Sanchez, Oscar; Soler, Juan (2004), Asymptotic Behaviour for the Vlasov-Poisson System in the Stellar-Dynamics Case, Archive for Rational Mechanics and Analysis, 171, 3, p. 301-327. http://dx.doi.org/10.1007/s00205-003-0283-4
TypeArticle accepté pour publication ou publié
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)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.
Subjects / Keywordslarge-time asymptotics; kinetic and potential energies; Vlasov-Poisson (VP) system
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