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A singular perturbation problem in a systemof nonlinear Schrödinger equation occurring in Langmuir turbulence

Published online by Cambridge University Press:  15 April 2002

Cédric Galusinski
Cédric Galusinski*
Affiliation:
Université Bordeaux I, Mathématiques Appliquées Bordeaux, ESA 5466 CNRS, 351 cours de la libération, 33400 Talence, France. (galusins@math.u-bordeaux.fr)
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Abstract

The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system $ i \partial_t E+\nabla (\nabla . E)-\alpha^2 \nabla \times \nabla \times E =-|E|^{2\sigma}E, $ where $E:{\ensuremath{{\Bbb R}}}^3\rightarrow{\mathbb C}^3$. This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the $H^1({\ensuremath{{\Bbb R}}}^3)$ norm.

Keywords

Nonlinear Schrödinger equationsingular perturbation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 109 - 125
Copyright
© EDP Sciences, SMAI, 2000

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References

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