Long time behaviour for generalized complex Ginzburg–Landau equation

In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL) ut = ρu − ϕ(u) −(1+iγ ) u −ν 2u− (1+ iμ)|u|2σ u +αλ1 · ∇ |u|2u + β(λ2 · ∇)|u|2 is studied. The existence of global attractor for this equation with periodic boundary condition is established and upper bounds of Hausdorff and fractal dimensions of attractor are obtained. © 2006 Elsevier Inc. All rights reserved.