  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
