Asymptotically autonomous dynamics for non-autonomous stochastic 2D g-Navier–Stokes equation in regular spaces

Abstract

This work is a continuation of our previous work [Li et al., Commun. Pure Appl. Anal. 19, 3137 (2020)] on the regular backward compact random attractor. We prove that under certain conditions, the components of the random attractor of a non-autonomous dynamical system can converge in time to those of the random attractor of the limiting autonomous dynamical system in more regular spaces rather than the basic phase space. As an application of the abstract theory, we show that the backward compact random attractors [∪s≤τA(s,ω) is precompact for each τ∈R] for the non-autonomous stochastic g-Navier–Stokes (g-NS) equation is backward asymptotically autonomous to a random attractor of the autonomous g-NS equation under the topology of H0,g1(O)2.