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A singular perturbation problem in a systemof nonlinear Schrödinger equation occurring in Langmuir turbulence
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 1 / January 2000
- Published online by Cambridge University Press:
- 15 April 2002, pp. 109-125
- Print publication:
- January 2000
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- Article
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The aim of this work is to establish, from amathematical 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 approximationwhich is made in the context of Langmuir turbulence in plasmaPhysics. The L 2-subcritical σ (that is σ ≤ 2/3)and the H 1-subcritical σ (that is σ ≤ 2) arestudied. In the physical case σ = 1, the limit is then studied for the $H^1({\ensuremath{{\Bbb R}}}^3)$ 
norm.
