Random attractors for the two-dimensional stochastic g-Navier-Stokes equations

The main objective of this paper is to study the long-time behaviour of solutions for the two-dimensional stochastic g-Navier-Stokes equations. Thanks to the shortage of the existence proof of random absorbing sets in a more regular phase space than V, we cannot directly obtain some kind of compactness in V of the cocycle by the Sobolev compactness embedding theorem. In this paper, we prove the existence of random attractors in H and V by using Sobolev Compactness Embedding Theorem and verifying the pullback flattening property, respectively.