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.

中文翻译：

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二维随机g-Navier-Stokes方程的随机吸引子

本文的主要目的是研究二维随机g-Navier-Stokes方程解的长期行为。由于缺乏比常规规则空间中的随机吸收集存在的证据$V$，我们不能直接在 $V$Sobolev紧致嵌入定理确定了余弦。在本文中，我们证明了随机吸引子的存在$H$ 和 $V$ 通过使用Sobolev紧致度嵌入定理并分别验证回拉展平性。