(untitled) (Journal of Partial Differential Equations, 2003)
" In this paper, we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = 03c1u + (1 + i03d2 )00010394u - (1 + i03bc) |u|^203c3 u, qquad(1) u(0, x) = u_0(x), qquad(2) where u is an unknown complex-value function defined in 3+1 dimensional space-time R^3+1, 0394 is a Laplacian in R00b3, 03c1 > 0, 03d2, 03bc are real parameters. 03a9 2208 R00b3 is a bounded domain. We show that the semigroup S(t) associated with the problem (1), (2) satisfies Lipschitz continuity and the squeezing property for the initial-value problem (1), (2) with the initial-value condition belonging to H00b2(03a9 ), therefore we obtain the existence of exponential attractor."