Large Time Behavior Of The Nonlocal Kuramoto-sivashinsky Equation Spectral Approximation And Its Dimension Is Estimated

Recently, more and more attentions are paid to the study of nonlinear fourth order parabolic equation with a nonlocal term equation. Mostly, more attentions are paid to their numerical simulations , for the equation's exact solution can't be gotten. The main purpose of this work is to investigate the long-time behaviors of Fourier spectral approximation to nonlocal Kuramoto-Sivashinsky equation.Firstly, we construct semi- discrete and fully discrete Fourier spectral scheme and priori estimates and prove the stability of semi- discrete Fourier spectral scheme.At same time we discuss their error estimate.the existence of approximate attractors A_N~k and the upper semi-continuity on A which is a global attractor of initial problem. Secondly we got the upper bounds of Hausdroff and fractral dimensions of A and A_N~k. At last, the uniform upper bounds for the Hausdroff of the (discrete)attractor are obtained.