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 (2010)

  • 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 36.6 (2010): 1071-1090. <http://eudml.org/doc/194140>.

@article{Puel2010,
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},
keywords = {Quasi-neutral plasmas; semi-classical limit; modulated energy.; quasi-neutral plasmas; modulated energy},
language = {eng},
month = {3},
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/194140},
volume = {36},
year = {2010},
}

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
DA - 2010/3//
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.; quasi-neutral plasmas; modulated energy
UR - http://eudml.org/doc/194140
ER -

References

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  2. Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations25 (2000) 737-754.  Zbl0970.35110
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  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. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthiers-Villars, Paris (1969).  Zbl0189.40603
  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).  
  8. P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoamericana9 (1993) 553-618.  Zbl0801.35117
  9. P.A. Markowich and N.J. Mauser, The classical limit of a self-consistent quantum-Vlasov equation in 3D. Math. Models Methods Appl. Sci.3 (1993) 109-124.  Zbl0772.35061
  10. M. Puel, Convergence of the Schrödinger-Poisson system to the incompressible Euler equations. Preprint LAN, Université Paris VI (2001).  
  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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