no. 9-10
Partial Differential Equations
Solutions of the Vlasov–Maxwell–Boltzmann system with long-range interactions
[Solutions du système de Vlasov–Maxwell–Boltzmann avec interactions à longue portée]

Présenté par : Pierre-Louis Lions

Arsénio, Diogo1 ; Saint-Raymond, Laure2
1 Institut de mathématiques, Université Paris-7–Denis-Diderot, Paris, France
2 Département de mathématiques et applications, École normale supérieure, Paris, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 357-360.

Nous établissons lʼexistence de solutions renormalisées du système de Vlasov–Maxwell–Boltzmann avec mesure de défaut en présence dʼinteractions à longue portée. Nous présentons également un contrôle de la mesure de défaut par la dissipation dʼentropie uniquement, qui sʼavère être crucial dans lʼétude des limites hydrodynamiques.

We establish the existence of renormalized solutions of the Vlasov–Maxwell–Boltzmann system with a defect measure in the presence of long-range interactions. We also present a control of the defect measure by the entropy dissipation only, which turns out to be crucial in the study of hydrodynamic limits.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.04.025
Arsénio, Diogo 1 ; Saint-Raymond, Laure 2

1 Institut de mathématiques, Université Paris-7–Denis-Diderot, Paris, France
2 Département de mathématiques et applications, École normale supérieure, Paris, France 
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Arsénio, Diogo; Saint-Raymond, Laure. Solutions of the Vlasov–Maxwell–Boltzmann system with long-range interactions. Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 357-360. doi : 10.1016/j.crma.2013.04.025. http://www.numdam.org/articles/10.1016/j.crma.2013.04.025/

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