Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T22:39:59.420Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  15 January 2003

Marjolaine Puel
Marjolaine Puel*
Affiliation:
Laboratoire d'analyse numérique (B 187), Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France. mpuel@ann.jussieu.fr.
Get access

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.

Keywords

Quasi-neutral plasmassemi-classical limitmodulated energy.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 1071 - 1090
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arnold, A. and Nier, F., The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Math. Methods Appl. Sci. 14 (1991) 595-613. CrossRef
Brenier, Y., Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations 25 (2000) 737-754. CrossRef
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).
Gérard, P., Markowich, P.A., Mauser, N.J. and Poupaud, F., Homogenization limits and Wigner transforms. Comm. Pure Appl. Math. 50 (1997) 323-379. 3.0.CO;2-C>CrossRef
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).
Lions, P.-L. and Paul, T., Sur les mesures de Wigner. Rev. Mat. Iberoamericana 9 (1993) 553-618. CrossRef
Markowich, P.A. and Mauser, N.J., The classical limit of a self-consistent quantum-Vlasov equation in 3D. Math. Models Methods Appl. Sci. 3 (1993) 109-124. CrossRef
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).