Global existence and attractors for the two-dimensional Burgers-Ginzburg- Landau equations

Volume 10, Issue 6, pp 3123--3135 http://dx.doi.org/10.22436/jnsa.010.06.27

Publication Date: June 25, 2017 Submission Date: February 06, 2017

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Authors

Changhong Guo - School of Management, Guangdong University of Technology, Guangzhou 510520, P. R. China. Shaomei Fang - Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.

Abstract

This paper investigates the periodic initial value problem for the two-dimensional Burgers-Ginzburg-Landau (2D Burgers- GL) equations, which can be derived from the so-called modulated modulation equations (MME) that govern the dynamics of the modulated amplitudes of some periodic critical modes. The well-posedness of the solutions and the global attractors for the 2D Burgers-GL equations are obtained via delicate a priori estimates, the Galerkin method, and operator semigroup method.

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Keywords

• invex set
• well-posedness
• global attractors
• a priori estimates.

MSC

•  35D35
•  35B41
•  35Q56

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