Bi-Lipschitz Mane projectors and finite-dimensional reduction for complex Ginzburg-Landau equation
arXiv:2002.05053 · doi:10.1098/rspa.2020.0144
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.