Inviscid limit behavior of solution for the multi-dimensional derivative complex  Ginzburg-Landau equation

Yueling Jia; Zhaohui Huo

doi:10.3934/krm.2014.7.57

Article Contents

2014, Volume 7, Issue 1: 57-77. Doi: 10.3934/krm.2014.7.57

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Inviscid limit behavior of solution for the multi-dimensional derivative complex Ginzburg-Landau equation

Yueling Jia^1, and
Zhaohui Huo^2,

1.
Institute of Applied Physics and Computational Mathematics, Beijing, 100094
2.
Institute of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190

Received: August 31, 2013

Revised: September 30, 2013

Published: February 2014

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Abstract

The inviscid limit behavior of solution is considered for the multi-dimensional derivative complex Ginzburg-Landau(DCGL) equation. For small initial data, it is proved that for some $T>0$, solution of the DCGL equation converges to the solution of the derivative nonlinear Schrödinger (DNLS) equation in natural space $C([0,T]; H^s)(s\geq \frac{n}{2})$ if some coefficients tend to zero.

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Mathematics Subject Classification: Primary: 35E15, 35K15, 35K55; Secondary: 35Q55.

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