Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II
[Limite quasineutre du système d’Euler-Poisson pour les ions dans un domaine à bord II]
Gérard-Varet, David1 ; Han-Kwan, Daniel2 ; Rousset, Frédéric3
1 Institut de Mathématiques de Jussieu (UMR 7586), Université Paris-Diderot Bâtiment Sophie Germain, 75205 Paris Cedex 13, France
2 CNRS & Centre de Mathématiques Laurent Schwartz (UMR 7640), École polytechnique 91128 Palaiseau Cedex, France
3 Laboratoire de Mathématiques d’Orsay (UMR 8628), Université Paris-Sud et Institut Universitaire de France Bâtiment 425, 91405 Orsay Cedex, France
Journal de l’École polytechnique - Mathématiques, Tome 1 (2014), pp. 343-386.

Dans cet article, nous étudions la limite quasineutre du système d’Euler-Poisson pour les ions dans un domaine à bord. Il s’agit de la suite de notre travail précédent [5], qui était consacré aux cas de conditions limites de type non-pénétration ou sortantes subsoniques. Nous nous focalisons ici sur le cas des vitesses sortantes supersoniques. La structure des couches limites ainsi que le mécanisme de stabilisation sont différents.

In this paper, we study the quasineutral limit of the isothermal Euler-Poisson equation for ions, in a domain with boundary. This is a follow-up to our previous work [5], devoted to no-penetration as well as subsonic outflow boundary conditions. We focus here on the case of supersonic outflow velocities. The structure of the boundary layers and the stabilization mechanism are different.

DOI : 10.5802/jep.13
Classification : 76N20, 76X05
Keywords: Isothermal Euler-Poisson equations, quasineutral limit, boundary layers, supersonic boundary conditions
Mot clés : Équations d’Euler-Poisson isothermes, limite quasineutre, couches limites, conditions aux limites supersoniques
Gérard-Varet, David 1 ; Han-Kwan, Daniel 2 ; Rousset, Frédéric 3

1 Institut de Mathématiques de Jussieu (UMR 7586), Université Paris-Diderot Bâtiment Sophie Germain, 75205 Paris Cedex 13, France
2 CNRS & Centre de Mathématiques Laurent Schwartz (UMR 7640), École polytechnique 91128 Palaiseau Cedex, France
3 Laboratoire de Mathématiques d’Orsay (UMR 8628), Université Paris-Sud et Institut Universitaire de France Bâtiment 425, 91405 Orsay Cedex, France 
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     title = {Quasineutral limit of the {Euler-Poisson} system for ions in a domain with boundaries {II}},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique - Math\'ematiques},
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Gérard-Varet, David; Han-Kwan, Daniel; Rousset, Frédéric. Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II. Journal de l’École polytechnique - Mathématiques, Tome 1 (2014), pp. 343-386. doi : 10.5802/jep.13. http://www.numdam.org/articles/10.5802/jep.13/

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