@Article{JPDE-16-2,
author = {},
title = {Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions},
journal = {Journal of Partial Differential Equations},
year = {2003},
volume = {16},
number = {2},
pages = {97--110},
abstract = { 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.},
issn = {2079-732X},
doi = {https://doi.org/2003-JPDE-5409},
url = {https://global-sci.com/article/88576/exponential-attractor-for-complex-ginzburg-landau-equation-in-three-dimensions}
}