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Julien Barré; David Chiron; Thierry Goudon; Nader Masmoudi
From Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck systems to incompressible Euler equations: the case with finite charge
(Des équations de Vlasov-Poisson et Vlasov-Poisson-Fokker-Planck aux équations d’Euler incompressibles : le cas de charge finie)
Journal de l'École polytechnique — Mathématiques, 2 (2015), p. 247-296, doi: 10.5802/jep.24
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Class. Math.: 82D10, 35Q35, 82C40
Mots clés: Physique des plasmas, système de Vlasov-Poisson, système de Vlasov-Poisson-Fokker-Planck, équations d’Euler incompressibles, équation des lacs, régime quasi-neutre, énergie modulée, entropie relative

Résumé - Abstract

Nous étudions le régime asymptotique de forts champs électriques qui conduit du système de Vlasov-Poisson aux équations d’Euler incompressibles. Nous abordons aussi le système de Vlasov-Poisson-Fokker-Planck qui induit des effets dissipatifs additionnels. L’originalité de cette étude réside dans le fait qu’on suppose la charge totale finie et confinée par un fort champ extérieur. En conséquence, l’équation limite est posée dans un domaine borné dont la géométrie est déterminée par ce champ confinant. L’analyse s’étend au cas où la densité limite est inhomogène ; l’équation d’Euler est alors remplacée par l’équation des lacs (ou modèle anélastique).

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