Abstract
We study the asymptotic behavior of solutions to a class of abstract nonlinear stochastic evolution equations with additive noise that covers numerous 2D hydrodynamical models, such as the 2D Navier–Stokes equations, 2D Boussinesq equations, 2D MHD equations, etc., and also some 3D models, like the 3D Leray 𝛼-model. We prove the existence of random attractors for the associated continuous random dynamical systems. We also establish the upper semicontinuity of the random attractors as the parameter tends to zero.
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