INERTIAL MANIFOLDS VIA SPATIAL AVERAGING REVISITED

Abstract

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by Sell and 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 sixth order Cahn-Hilliard equations, and several classes of modified Navier-Stokes equations, including the Leray-α regularization, hyperviscous regularization, and their combinations. All of the results are obtained in three-dimensional case with periodic boundary conditions.