Mean asymptotic behavior for stochastic Kuramoto–Sivashinshy equation in Bochner spaces

Abstract

This paper is concerned with the mean asymptotic behavior of the Kuramoto–Sivashinshy equation with stochastic perturbation. We define the mean random dynamical systems for the stochastic Kuramoto–Sivashinshy equation in Bochner spaces. Then we obtain the so-called weak pullback mean random attractor for the stochastic Kuramoto–Sivashinshy equation with odd initial conditions.