Asymptotic autonomy of bi-spatial attractors for stochastic retarded Navier-Stokes equations

Abstract

We establish semi-convergence of a non-autonomous bi-spatial random attractor towards to an autonomous attractor under the topology of the regular space when time-parameter goes to infinity, where the criteria are given by forward compactness of the attractor in the terminal space as well as forward convergence of the random dynamical system in the initial space. We then apply to both non-autonomous and autonomous stochastic 2D Navier-Stokes equations with general delays (including variable and distribution delays). The forward-pullback asymptotic compactness in the space of continuous Sobolev-valued functions is proved by the method of spectrum decomposition.