Fourier Spectral Approximation to Global Attractor for 2D Convective Cahn–Hilliard Equation

Abstract

In this paper, we consider the long-time behavior of the convective Cahn–Hilliard equation in 2D case. A linear fully discrete Galerkin–Fourier spectral approximation scheme is constructed and the existence of the global attractors of the discrete system is obtained. All results in this paper are obtained without any restriction on the time step size.