Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 36, Issue: 6, page 1071-1090
- ISSN: 0764-583X
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topPuel, 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
top- 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.
- Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations25 (2000) 737-754.
- T. Cazenave, An introduction to nonlinear Schrödinger equations, in: Textos de méthodos Mathemàticas 26. Universidad Federal do Rio de Janeiro (1993).
- C. Cohen-Tannoudji, B. Diu and F. Laloë, Mécanique quantique. Hermann (1973).
- P. Gérard, P.A. Markowich, N.J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms. Comm. Pure Appl. Math.50 (1997) 323-379.
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthiers-Villars, Paris (1969).
- 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).
- P.-L. Lions and T. Paul, Sur les mesures de Wigner. Rev. Mat. Iberoamericana9 (1993) 553-618.
- 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.
- M. Puel, Convergence of the Schrödinger-Poisson system to the incompressible Euler equations. Preprint LAN, Université Paris VI (2001).
- 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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