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arXiv · 2002.05053

Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation

Anna Kostianko
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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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Anna Kostianko. 2020-02-12. Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation. https://doi.org/10.1098/rspa.2020.0144

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