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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 2
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Original Articles

Well-posedness and dynamics for the fractional Ginzburg-Landau equation

Xueke Pu College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P.R. ChinaCorrespondence[email protected]
&
Boling Guo Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
Pages 318-334 | Received 03 Jun 2011, Accepted 02 Aug 2011, Published online: 14 Sep 2011
 
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Abstract

This article studies the global well-posedness and long-time dynamics for the nonlinear complex Ginzburg–Landau equation involving fractional Laplacian. The global existence and some uniqueness criterion of weak solutions are given with compactness method. To study the strong solutions with the semigroup method, we generalize some pointwise estimates for the fractional Laplacian to the complex background and study carefully the linear evolution of the equation. Finally, the existence of global attractors is studied.

AMS Subject Classification:

Acknowledgements

Supported by the NNSF of China under Grant No. 11001285.

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