The asymptotic behavior of a model for 2D incompressible stochastic micropolar fluid flows with rough noise on a Poincaré domain is investigated. First, the existence and uniqueness of solutions to an evolution equation arising from the underlying stochastic micropolar fluid model is established via the Galerkin method and energy method. Then the existence of a random attractor is studied by using the theory of random dynamical systems for which the noise is dealt with by appropriate reproducing kernel Hilbert space.

中文翻译：

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二维随机微极性流体在无界域上的随机吸引子

研究了庞加莱域上具有粗糙噪声的二维不可压缩随机微极性流体流动模型的渐近行为。首先，通过伽勒金法和能量法建立了由潜在的随机微极性流体模型产生的演化方程解的存在性和唯一性。然后利用随机动力系统理论研究了随机吸引子的存在，通过适当的再生核希尔伯特空间来处理噪声。