Uniform random attractors for 2D non-autonomous stochastic Navier-Stokes equations

Abstract

In this paper, we first establish the existence of uniform random attractor for 2D stochastic Navier-Stokes equation in H with deterministic non-autonomous external force being normal in Lloc2(R;V′), which is the measurable minimal compact set and uniformly attracts bounded random set in H in the sense of pullback. We also show that uniform random attractor with respect to the deterministic non-autonomous functions belonging to some symbol space coincides with uniform random attractor with respect to the initial time. Then we show that the uniform random attractor for the equation under consideration has regularity property in V when deterministic non-autonomous external force being normal in Lloc2(R;H).