Quasineutral limit for Vlasov-Poisson with Penrose stable data

Han-Kwan, Daniel; Rousset, Frédéric

doi:10.24033/asens.2313

Quasineutral limit for Vlasov-Poisson with Penrose stable data
[Limite quasi neutre pour Vlasov-Poisson avec des données stables au sens de Penrose]

Han-Kwan, Daniel ; Rousset, Frédéric

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 6, pp. 1445-1495.

Résumé
Abstract

Nous étudions la limite quasineutre d'un système de Vlasov-Poisson qui décrit la dynamique d'ions dans un plasma. Nous travaillons avec des données à régularité Sobolev sous l'hypothèse optimale que les profils en vitesse des données initiales satisfont une condition de stabilité de Penrose.

Comme corollaire de notre analyse, nous obtenons une théorie d'existence et d'unicité pour l'équation limite (qui est une équation de Vlasov avec une mesure de Dirac pour noyau d'interaction), pour de telles données.

We study the quasineutral limit of a Vlasov-Poisson system that describes the dynamics of ions in a plasma. We handle data with Sobolev regularity under the sharp assumption that the profiles in velocity of the initial data satisfy a Penrose stability condition.

As a byproduct of our analysis, we obtain a well-posedness theory for the limit equation (which is a Vlasov equation with Dirac measure as interaction kernel), for such data.

Publié le : 2016-11-15

DOI : 10.24033/asens.2313

Classification : 35Q83, 35Q35
Keywords: Vlasov-Poisson, quasineutral limit, Penrose stability condition.
Mot clés : Vlasov-Poisson, limite quasi neutre, condition de stabilité de Penrose.

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     author = {Han-Kwan, Daniel and Rousset, Fr\'ed\'eric},
     title = {Quasineutral limit for {Vlasov-Poisson} with {Penrose} stable data},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1445--1495},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 49},
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Han-Kwan, Daniel; Rousset, Frédéric. Quasineutral limit for Vlasov-Poisson with Penrose stable data. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 6, pp. 1445-1495. doi : 10.24033/asens.2313. http://www.numdam.org/articles/10.24033/asens.2313/

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