论文标题
在有限域中，2D随机对流的Brinkman-Forchheimer方程的随机吸引子的存在和上半接触率
Existence and upper semicontinuity of random attractors for the 2D stochastic convective Brinkman-Forchheimer equations in bounded domains
论文作者
论文摘要
在这项工作中，我们讨论了有限域中二维随机对流Brinkman-Forchheimer（SCBF）方程的大量时间行为。在功能设置下，$ \ v \ hookrightArrow \ h \ hookrightArrow \ v'$，其中$ \ h $和$ \ v $是合适的可分离的希尔伯特空间，并且嵌入$ \ v \ v \ hookrightArrow \ h $是紧凑的，我们在$ \ h $中的随机吸引者在$ \ h $中的随机吸引者的存在，该方程是由$ \ h $ scochative生成的。当随机术语的系数接近零时，我们证明了2D SCBF方程的随机吸引子的上半接口。此外，我们使用回调扁平属性在更常规的空间$ \ v $中获得了随机吸引子的存在。随机吸引子的存在可确保存在不变的紧凑型随机集，因此我们显示了对2D SCBF方程的不变度度量。
In this work, we discuss the large time behavior of the solutions of the two dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations in bounded domains. Under the functional setting $\V\hookrightarrow\H\hookrightarrow\V'$, where $\H$ and $\V$ are appropriate separable Hilbert spaces and the embedding $\V\hookrightarrow\H$ is compact, we establish the existence of random attractors in $\H$ for the stochastic flow generated by the 2D SCBF equations perturbed by small additive noise. We prove the upper semicontinuity of the random attractors for the 2D SCBF equations in $\H$, when the coefficient of random term approaches zero. Moreover, we obtain the existence of random attractors in a more regular space $\V$, using the pullback flattening property. The existence of random attractors ensures the existence of invariant compact random set and hence we show the existence of an invariant measure for the 2D SCBF equations.
