Pullback Measure Attractors for Non-autonomous Stochastic 3D Globally Modified Navier–Stokes Equations

This paper investigates the existence and upper semi-continuity of the pullback measure attractors of the non-autonomous stochastic 3D globally modified Navier–Stokes equations driven by nonlinear noise. Firstly, we introduce the abstract theory of pullback measure attractors and asymptotic compactness of such equations. Then, the existence of the pullback measure attractors is shown for such equations. Furthermore, the upper semi-continuity of these attractors is also obtained as the noise intensity tends to zero.