Multi-dimensional Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on admissible multi-dimensional domains

Abstract

An initial-boundary value problem for the n-dimensional ($n$ is a natural number from the interval [2,7]) Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on smooth bounded domains in ${\mathbb{R}}^n$ was considered. The existence and uniqueness of global regular solutions as well as their exponential decay have been established. A connection between an order of the stationary part of the equation and admissible dimensions of a domain has been revealed. Keywords: Kuramoto-Sivashinsky equation, Zakharov-Kuznetsov equation, Global solutions

arXiv admin note: text overlap with arXiv:2203.14739