EXPONENTIAL ATTRACTOR FOR COMPLEX GINZBURG—LANDAU EQUATION IN THREE—DIMENSIONS

摘要

In this paper,we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions ut=ρu+(1+iγ)△u-1+iμ—|u|^2σu,(1) u(0,x)=u0(x),(2) where u is an unknown complex-value function defined in 3+1 dimensional space-time R^3+1,△ is a Laplacian in R^3,ρ>0,γ,μ are real parameters,Ω∈R^3 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 H^2(Ω）,therefore we obtain the existence of exponential attractor.