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Taylor and Francis Group, Communications in Partial Differential Equations, 10(31), p. 1425-1449

DOI: 10.1080/03605300500481517

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Stability for the Gravitational Vlasov–Poisson System in Dimension Two

Journal article published in 2006 by Jean Dolbeault ORCID, Javier Fernandez, Óscar Sánchez, O. Sanchez
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This paper is available in a repository.

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Abstract

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.