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 , we cannot directly obtain some kind of compactness in of the cocycle by the Sobolev compactness embedding theorem. In this paper, we prove the existence of random attractors in and by using Sobolev Compactness Embedding Theorem and verifying the pullback flattening property, respectively.