Dynamics of the stochastic velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

In this paper, we study the asymptotic behavior of solutions of the non-autonomous stochastic velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory driven by multiplicative white noise. We first show the existence of pullback random attractors when the intensity of noise is sufficiently small. Then we show the upper semicontinuity of random attractors when the intensity of noise approaches zero. To the best of our knowledge, this is the first attempt to establish the existence as well as the upper semicontinuity of random attractors for the non-autonomous stochastic velocity-vorticity-Voigt model.