[Limite quasineutre du système d’Euler-Poisson pour les ions dans un domaine à bord II]
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.
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
@article{JEP_2014__1__343_0,
author = {G\'erard-Varet, David and Han-Kwan, Daniel and Rousset, Fr\'ed\'eric},
title = {Quasineutral limit of the {Euler-Poisson} system for ions in a domain with boundaries {II}},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {343--386},
publisher = {Ecole polytechnique},
volume = {1},
year = {2014},
doi = {10.5802/jep.13},
zbl = {06275539},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jep.13/}
}
TY - JOUR AU - Gérard-Varet, David AU - Han-Kwan, Daniel AU - Rousset, Frédéric TI - Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II JO - Journal de l’École polytechnique — Mathématiques PY - 2014 SP - 343 EP - 386 VL - 1 PB - Ecole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.13/ DO - 10.5802/jep.13 LA - en ID - JEP_2014__1__343_0 ER -
%0 Journal Article %A Gérard-Varet, David %A Han-Kwan, Daniel %A Rousset, Frédéric %T Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II %J Journal de l’École polytechnique — Mathématiques %D 2014 %P 343-386 %V 1 %I Ecole polytechnique %U http://www.numdam.org/articles/10.5802/jep.13/ %R 10.5802/jep.13 %G en %F JEP_2014__1__343_0
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/
[1] Stability for solutions of a stationary Euler-Poisson problem, Math. Models Methods Appl. Sci., Volume 16 (2006) no. 11, pp. 1817-1837 | DOI | MR | Zbl
[2] On singular perturbation problems for the nonlinear Poisson equation, Asymptot. Anal., Volume 25 (2001) no. 1, pp. 39-91 | MR | Zbl
[3] Multidimensional hyperbolic partial differential equations, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, Oxford, 2007, pp. xxvi+508 (First-order systems and applications) | MR | Zbl
[4] Quasineutral limit of an Euler-Poisson system arising from plasma physics, Comm. Partial Differential Equations, Volume 25 (2000) no. 5-6, pp. 1099-1113 | DOI | MR | Zbl
[5] Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries, Indiana Univ. Math. J., Volume 62 (2013), pp. 359-402 | MR
[6] Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Anal., Volume 95 (1986) no. 4, pp. 325-344 | DOI | MR | Zbl
[7] Principles of plasma discharges and materials processing, Cambridge University Press, 1994
[8] Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics, SIAM J. Math. Anal., Volume 44 (2012) no. 2, pp. 761-790 | DOI | MR | Zbl
[9] The Bohm criterion and sheath formation, J. Phys. D: Applied Physics, Volume 24 (1991) no. 4, pp. 493
[10] Quasi-neutral limit for Euler-Poisson system, J. Nonlinear Sci., Volume 11 (2001) no. 3, pp. 193-209 | DOI | MR | Zbl
[11] Asymptotic stability of stationnary solutions to the Euler-Poisson equations arising in plasma physics, Kinet. and Relat. Mod., Volume 4 (2011) no. 2, pp. 569-588 | MR | Zbl
Cité par Sources :
