A new sharp estimate on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg-Landau equation

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Karachalios, Nikos I.
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Abstract
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Using the improved lower bound on the sum of the eigenvalues of the Dirichlet Laplacian proved by A. D. Melas (Proc. Amer. Math. Soc. \textbf{131} (2003) 631-636), we report a new and sharp estimate for the dimension of the global attractor associated to the complex Ginzburg-Landau equation supplemented with Dirichlet boundary conditions.
Comment: 5 pages
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Mathematics - Analysis of PDEs, Mathematical Physics, 35Q55, 35B40, 35B41, 37L30
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