Random attractors for stochastic 2D hydrodynamical type systems

The Anh Cung; Tien Da Nguyen

The Anh Cung Hanoi Nat. Univ. Education, Vietnam https://orcid.org/0000-0002-5669-334X
Tien Da Nguyen

Keywords: Random attractors; stochastic 2D hydrodynamical type systems; upper semicontinuity; energy equation arguments

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 $\alpha$-model.
We prove the existence of random attractors for the associated continuous random dynamical systems.
Then we establish the upper semicontinuity of the random attractors as the parameter tends to zero.

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