论文标题
弱的回调平均随机吸引子，用于随机对流Brinkman-Forchheimer方程和局部单调随机偏微分方程
Weak pullback mean random attractors for the stochastic convective Brinkman-Forchheimer equations and locally monotone stochastic partial differential equations
论文作者
论文摘要
这项工作关注的是由白噪声和非线性扩散项驱动的两个和三维随机对流Brinkman-Forchheimer（SCBF）方程的渐近行为。我们证明了弱回调的存在和独特性，平均随机吸引子（对于$ r \ geq1 $）以及3D SCBF方程（对于$ r> 3 $，$ r> 3 $，任何$μ，β> 0 $和$ r = 3 $，$ r = 3 $，$2μβ\ geq1 $）在bochner的空间中，当时$2μβ\ geq1 $）此外，我们为一类局部单调的随机部分偏微分方程的弱回调平均随机吸引子的存在。
This work is concerned about the asymptotic behavior of the solutions of the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations driven by white noise with nonlinear diffusion terms. We prove the existence and uniqueness of weak pullback mean random attractors for the 2D SCBF equations (for $r\geq1$) as well as 3D SCBF equations (for $r>3$, any $μ,β>0$ and for $r=3$, $2μβ\geq1$) in Bochner spaces, when the diffusion terms are Lipschitz nonlinear functions. Furthermore, we establish the existence of weak pullback mean random attractors for a class of locally monotone stochastic partial differential equations.
