Global Regular Solutions for the Multi-dimensional Kuramoto-Sivashinsky Equation posed on Smooth Domains

Abstract

Initial-boundary value problems for the $n$-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky equation posed on smooth bounded domains in ${\mathbb{R}}^n$ were considered. The existence and uniqueness of global regular solutions as well as their exponential decay have been considered.