Local uniformly upper semi-continuity of random attractor for g-Navier–Stokes equation

Journal of Mathematical Physics, Volume 61, Issue 10, October 2020. This paper is concerned with the locally uniform convergence from a family of pullback random attractors to a deterministic attractor. We establish criteria by using joint-pathwise convergence of the cocycles, collective locally uniform compactness, and eventually deterministic of the random attractors. As an application of the abstract result, it is shown that the family of random attractors for the stochastic g-Navier–Stokes equation is local uniformly upper semi-continuous as the density of random noise tends to zero.