Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation

Abstract

We study the fractional complex Ginzburg-Landau equation with periodic initial boundary value condition in three spatial dimensions. The problem is discretized fully by Fourier Galerkin spectral method. The dynamical behavior of the resulting discrete system is examined. The existence of a global attractor is established, and the corresponding convergence is proved through the error estimates of the discrete solution. Numerical stability and convergence of the discrete scheme are proved.