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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
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.
- 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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