Volume 16, Issue 2
Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions

Boling Guo & Donglong Li

DOI:

J. Part. Diff. Eq., 16 (2003), pp. 97-110.

Published online: 2003-05

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  • 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.

  • Keywords

Ginzburg-Landau equation exponential attractor squeezing property

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@Article{JPDE-16-97, 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/}, url = {http://global-sci.org/intro/article_detail/jpde/5409.html} }
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