Global existence  for the Euler-Maxwell system

Germain, Pierre; Masmoudi, Nader

doi:10.24033/asens.2219

Global existence for the Euler-Maxwell system
[Existence globale pour le système d'Euler-Maxwell]

Germain, Pierre ; Masmoudi, Nader

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 3, pp. 469-503.

Résumé
Abstract

Le système d'Euler-Maxwell décrit l'évolution d'un plasma quand les collisions sont suffisamment importantes pour que chaque espèce soit dans un état d'équilibre hydrodynamique. On prouve dans cet article l'existence globale de petites solutions à ce système, posé en dimension 3 d'espace, en combinant la méthode des résonances en espace-temps (pour obtenir la décroissance des solutions) et des estimations d'énergie (pour contrôler la régularité des solutions). La décroissance non intégrable des solutions impose de combiner étroitement ces deux arguments en examinant le rôle des résonances au sein des estimations d'énergie.

The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the whole three-dimensional space, by combining the space-time resonance method (to obtain decay) and energy estimates (to control high frequencies). The non-integrable decay of the solutions makes it necessary to examine resonances within the energy estimate argument.

Publié le : 2014-09-24

MR Zbl

DOI : 10.24033/asens.2219

Classification : 35L03, 35L60, 35Q31, 35Q60, 37L50.
Keywords: Euler-Maxwell equations, global existence, space-time resonances.
Mot clés : Équations d'Euler-Maxwell, existence globale, résonances en espace-temps.

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     author = {Germain, Pierre and Masmoudi, Nader},
     title = {Global existence  for the {Euler-Maxwell} system},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {469--503},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 47},
     number = {3},
     year = {2014},
     doi = {10.24033/asens.2219},
     mrnumber = {3239096},
     zbl = {1311.35195},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2219/}
}

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Germain, Pierre; Masmoudi, Nader. Global existence  for the Euler-Maxwell system. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 3, pp. 469-503. doi : 10.24033/asens.2219. http://www.numdam.org/articles/10.24033/asens.2219/

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