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Stability for the gravitational Vlasov-Poisson system in dimension two

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Date
2006
Link to item file
http://hal.archives-ouvertes.fr/hal-00004799/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Vlasov-Poisson system; dynamical stability; Dirichlet boundary conditions; Uniqueness; Semilinear elliptic equations; Lagrange multiplier; minimizers; solutions with compact support; scalings; minimization; direct variational methods; bounded solutions; Riesz' theorem; symmetric nonincreasing rearrangements; optimal constants; Sobolev-Hardy-Littlewood inequality; interpolation; potential energy; kinetic energy; energy; mass; gravitation; polytropic gas spheres; stellar dynamics
Journal issue
Communications in Partial Differential Equations
Volume
31
Number
10
Publication date
10-2006
Article pages
1425-1449
Publisher
Taylor & Francis Group
DOI
http://dx.doi.org/10.1080/03605300500481517
URI
https://basepub.dauphine.fr/handle/123456789/763
Collections
  • CEREMADE : Publications
Metadata
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Author
Dolbeault, Jean
Fernandez, Javier
Sanchez, Oscar
Type
Article accepté pour publication ou publié
Abstract (EN)
Nous considérons en dimension deux le système de Vlasov-Poisson gravitationnel. Par des méthodes variationnelles, nous prouvons l'existence de solutions stationnaires d'énergie minimale sous une contrainte de type Casimir. La méthode donne aussi un résultat de stabilité de ces solutions pour le problème d'évolution. We consider the two dimensional gravitational Vlasov-Poisson system. Using variational methods, we prove the existence of stationary solutions of minimal energy under a Casimir type constraint. The method also provides a stability criterion of these solutions for the evolution problem.

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