This paper concerns the long term behavior of the stochastic two-dimensional g-Navier–Stokes equations with additive noise defined on a sequence of expanding domains, where the ultimate domain is unbounded and of Poincaré type. We prove that the weak continuity is uniform with respect to all expanding cocycles, which yields the equi-asymptotic compactness by using an energy equation method. Finally, we show the existence of a random attractor for the equation on each domain and the upper semi-continuity of random attractors as the bounded domain is expanded to the unbounded ultimate domain.

中文翻译：

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具有加性噪声的随机g -Navier–Stokes方程的随机吸引子的大域稳定性

本文涉及随机二维二维g-Navier-Stokes方程的长期行为，该方程具有在一系列扩展域上定义的加性噪声​​，其中最终域是无界的并且为Poincaré类型。我们证明了弱连续性对于所有扩展的cocycles是均匀的，这通过使用能量方程方法产生了等渐密性。最后，我们显示了在每个域上方程的一个随机吸引子的存在，以及当有界域扩展到无界最终域时随机吸引子的上半连续性。