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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

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Archive for Rational Mechanics and Analysis
Volume
171
Number
3
Publisher
Springer
Pages
301-327
Publication identifier
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Author(s)
Dolbeault, Jean cc
Sanchez, Oscar
Soler, Juan
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 / Keywords
large-time asymptotics; kinetic and potential energies; Vlasov-Poisson (VP) system