Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field

Marjolaine Puel

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 6, page 1071-1090
  • ISSN: 0764-583X

Abstract

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In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.

How to cite

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Puel, Marjolaine. "Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.6 (2002): 1071-1090. <http://eudml.org/doc/245343>.

@article{Puel2002,
abstract = {In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.},
author = {Puel, Marjolaine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quasi-neutral plasmas; semi-classical limit; modulated energy},
language = {eng},
number = {6},
pages = {1071-1090},
publisher = {EDP-Sciences},
title = {Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field},
url = {http://eudml.org/doc/245343},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Puel, Marjolaine
TI - Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 6
SP - 1071
EP - 1090
AB - In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.
LA - eng
KW - quasi-neutral plasmas; semi-classical limit; modulated energy
UR - http://eudml.org/doc/245343
ER -

References

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  1. [1] A. Arnold and F. Nier, The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Math. Methods Appl. Sci. 14 (1991) 595–613. Zbl0742.35078
  2. [2] Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations 25 (2000) 737–754. Zbl0970.35110
  3. [3] T. Cazenave, An introduction to nonlinear Schrödinger equations, in: Textos de méthodos Mathemàticas 26. Universidad Federal do Rio de Janeiro (1993). 
  4. [4] C. Cohen-Tannoudji, B. Diu and F. Laloë, Mécanique quantique. Hermann (1973). 
  5. [5] P. Gérard, P.A. Markowich, N.J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms. Comm. Pure Appl. Math. 50 (1997) 323–379. Zbl0881.35099
  6. [6] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthiers-Villars, Paris (1969). Zbl0189.40603MR259693
  7. [7] P.-L. Lions, Mathematical topics in fluid mechanics, Vol. 1. Incompressible models. Oxford Lecture in Mathematics and its Applications. Oxford University Press, New York (1996). Zbl0866.76002MR1422251
  8. [8] P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoamericana 9 (1993) 553–618. Zbl0801.35117
  9. [9] P.A. Markowich and N.J. Mauser, The classical limit of a self-consistent quantum-Vlasov equation in 3 D. Math. Models Methods Appl. Sci. 3 (1993) 109–124. Zbl0772.35061
  10. [10] M. Puel, Convergence of the Schrödinger-Poisson system to the incompressible Euler equations. Preprint LAN, Université Paris VI (2001). Zbl1040.35076MR1944031
  11. [11] M. Puel, Études variationnelle et asymptotique de problèmes en mécanique des fluides et des plasmas. Ph.D. thesis, Université Paris VI (2001). 

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