Regular dynamics of stochastic nondissipative retarded Kuramoto–Sivashinsky equations

Abstract

AbstractThe theme of this paper is to study the long‐term behavior of stochastic nondissipative Kuramoto–Sivashinsky (KS) equations with time‐dependent force and abstract delays. We first introduce an odd function to overcome the nondissipation of this equation. We then use the spectrum decomposition technique to prove the existence and regularity of a unique pullback random attractor (PRA), and establish the measurability, forward compactness, and long‐time stability of PRAs in the regular space. Finally, we consider the upper semicontinuity of PRAs in the regular space from nonautonomy to autonomy. Moreover, we provide three concrete examples for the general delay term.