Inertial Manifolds for the 3D Cahn-Hilliard Equations with Periodic Boundary Conditions

Abstract

The existence of an inertial manifold for the 3D Cahn-Hilliard equation with periodic boundary conditions is verified using the proper extension of the so-called spatial averaging principle introduced by G. Sell and J. Mallet-Paret. Moreover, the extra regularity of this manifold is also obtained.