Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II

David Gérard-Varet[1]; Daniel Han-Kwan[2]; Frédéric Rousset[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

Journal de l’École polytechnique — Mathématiques (2014)

  • Volume: 1, Issue: 2, page 343-386
  • ISSN: 2270-518X

Abstract

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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.

How to cite

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Gérard-Varet, David, Han-Kwan, Daniel, and Rousset, Frédéric. "Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II." Journal de l’École polytechnique — Mathématiques 1.2 (2014): 343-386. <http://eudml.org/doc/275499>.

@article{Gérard2014,
abstract = {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.},
affiliation = {Institut de Mathématiques de Jussieu (UMR 7586), Université Paris-Diderot Bâtiment Sophie Germain, 75205 Paris Cedex 13, France; CNRS & Centre de Mathématiques Laurent Schwartz (UMR 7640), École polytechnique 91128 Palaiseau Cedex, France; Laboratoire de Mathématiques d’Orsay (UMR 8628), Université Paris-Sud et Institut Universitaire de France Bâtiment 425, 91405 Orsay Cedex, France},
author = {Gérard-Varet, David, Han-Kwan, Daniel, Rousset, Frédéric},
journal = {Journal de l’École polytechnique — Mathématiques},
keywords = {Isothermal Euler-Poisson equations; quasineutral limit; boundary layers; supersonic boundary conditions; isothermal Euler-Poisson; modulated linearized energy},
language = {eng},
number = {2},
pages = {343-386},
publisher = {École polytechnique},
title = {Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II},
url = {http://eudml.org/doc/275499},
volume = {1},
year = {2014},
}

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
PB - École polytechnique
VL - 1
IS - 2
SP - 343
EP - 386
AB - 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.
LA - eng
KW - Isothermal Euler-Poisson equations; quasineutral limit; boundary layers; supersonic boundary conditions; isothermal Euler-Poisson; modulated linearized energy
UR - http://eudml.org/doc/275499
ER -

References

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  2. A. Ambroso, F. Méhats, P. A. Raviart, On singular perturbation problems for the nonlinear Poisson equation, Asymptot. Anal. 25 (2001), 39-91 Zbl0986.34051MR1814989
  3. S. Benzoni-Gavage, D. Serre, Multidimensional hyperbolic partial differential equations, (2007), The Clarendon Press Oxford University Press, Oxford Zbl1113.35001MR2284507
  4. S. Cordier, E. Grenier, Quasineutral limit of an Euler-Poisson system arising from plasma physics, Comm. Partial Differential Equations 25 (2000), 1099-1113 Zbl0978.82086MR1759803
  5. D. Gérard-Varet, D. Han-Kwan, F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries, Indiana Univ. Math. J. 62 (2013), 359-402 Zbl06275539MR3158514
  6. J. Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rational Mech. Anal. 95 (1986), 325-344 Zbl0631.35058MR853782
  7. M. Lieberman, A. Lichtenberg, Principles of plasma discharges and materials processing, (1994), Cambridge University Press 
  8. S. Nishibata, M. Ohnawa, M. Suzuki, Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics, SIAM J. Math. Anal. 44 (2012), 761-790 Zbl1257.35038MR2914249
  9. K-U Riemann, The Bohm criterion and sheath formation, J. Phys. D: Applied Physics 24 (1991) 
  10. M. Slemrod, N. Sternberg, Quasi-neutral limit for Euler-Poisson system, J. Nonlinear Sci. 11 (2001), 193-209 Zbl0997.34033MR1852940
  11. M. Suzuki, Asymptotic stability of stationnary solutions to the Euler-Poisson equations arising in plasma physics, Kinet. and Relat. Mod. 4 (2011), 569-588 Zbl1227.35073MR2786399

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