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On the Cauchy problem for the 1+2 complex Ginzburg-Landau equation

Published online by Cambridge University Press:  17 February 2009

Charles Bu
Charles Bu
Affiliation:
Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02181, U.S.A.
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Abstract

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We present analytical methods to investigate the Cauchy problem for the complex Ginzburg-Landau equation u1 = (v + iα)Δu − (κ + iβ) |u|2qu + γu in 2 spatial dimensions (here all parameters are real). We first obtain the local existence for v > 0, κ ≥ 0. Global existence is established in the critical case q = 1. In addition, we prove the global existence when .

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 3 , January 1995 , pp. 313 - 324
Copyright
Copyright © Australian Mathematical Society 1995

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