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Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation (2002.05053v1)

Published 12 Feb 2020 in math.AP

Abstract: We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mane projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of 3D complex Ginzburg-Landau equation with periodic boundary conditions. The method combines the so-called spatial-averaging principle invented by Sell and Mallet-Paret with temporal averaging of rapid oscillations which come from cross-diffusion terms.

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