Inertial manifolds via spatial averaging revisited
Analysis of PDEs
2020-06-30 v1
Abstract
The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number of new ones. Among our applications are reaction-diffusion equations, various types of generalized Cahn-Hilliard equations, including fractional and 6th order Cahn-Hilliard equations and several classes of modified Navier-Stokes equations including the Leray- regularization, hyperviscous regularization and their combinations. All of the results are obtained in 3D case with periodic boundary conditions.
Keywords
Cite
@article{arxiv.2006.15663,
title = {Inertial manifolds via spatial averaging revisited},
author = {Anna Kostianko and Xinhua Li and Chunyou Sun and Sergey Zelik},
journal= {arXiv preprint arXiv:2006.15663},
year = {2020}
}