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.

中文翻译：

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二维随机流体动力型系统的随机吸引子

我们研究了一类具有加性噪声的抽象非线性随机演化方程的解的渐近行为，这些方程涵盖了许多 2D 流体动力学模型，例如 2D Navier-Stokes 方程、2D Boussinesq 方程、2D MHD 方程等，以及一些 3D模型，例如 3D Leray 𝛼模型。我们证明了相关连续随机动力系统的随机吸引子的存在。我们还建立了随机吸引子的上半连续性，因为参数趋于零。