Long-time behaviour of the solutions for the multidimensional kolmogorov-spieqel-sivashinsky equation

摘要

In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the gevrey class regularity of the solutions and construct an approximate inertial manifold for the system.