Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610015 | Journal of Differential Equations | 2015 | 26 Pages |
Abstract
We study the initial boundary value problem of the fractional complex Ginzburg–Landau equation in three spatial dimensions with the dissipative effect given by a fractional Laplacian. A priori estimates are derived when the nonlinearity satisfies certain growth conditions. Using Galerkin's method, the existence of a global smooth solution is established. Uniqueness is also proved. Furthermore, the existence of a global attractor is proved, and estimates of the Hausdorff and fractal dimensions for the global attractor are obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hong Lu, Peter W. Bates, Shujuan Lü, Mingji Zhang,