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# Dynamics of Partial Differential Equations

## Volume 11 (2014)

### Number 1

### Regularity of attractor for 3D derivative Ginzburg-Landau equation

Pages: 89 – 108

DOI: http://dx.doi.org/10.4310/DPDE.2014.v11.n1.a5

#### Authors

#### Abstract

In this paper, we are concerned with a three-dimensional derivative Ginzburg-Landau equation with a periodic initial value condition. The smoothing property of the solution is established by a uniform priori estimates. The existence of the global attractors, $\mathcal{A}_i \subset H^i_p (\Omega) (i=2,3,\dots)$ for the semi-group ${ \{ S^{(i)} (t) \} }_{t \geq 0}$ of the operators generated by the equation is proved by using the compactness principle. Finally, the regularity of the global attractors, namely, $\mathcal{A}_2 = \mathcal{A}_3 = \dots = \mathcal{A}_m$, is proved by using the method of semi-group decomposition.

#### Keywords

Ginzburg-Landau equation, global attractor, regularity, Hölder inequality, priori estimates, semi-group decomposition

#### 2010 Mathematics Subject Classification

35B41, 35B45, 35Q56