TY - JOUR
T1 - Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions
JO - Journal of Partial Differential Equations
VL - 2
SP - 97
EP - 110
PY - 2003
DA - 2003/05
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5409.html
KW - Ginzburg-Landau equation
KW - exponential attractor
KW - squeezing property
AB -  In this paper, we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ
)
Δu - (1 + iμ) |u|^{2σ} 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}, Δ is a Laplacian in R³, ρ > 0, 
ϒ, μ are real parameters. Ω ∈ R³ 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 H²(Ω ), therefore we obtain the existence of exponential attractor.