论文标题
二维闭合歧管上的简化Bardina方程
The simplified Bardina equations on two-dimensional closed manifolds
论文作者
论文摘要
在本文中，我们研究了二维封闭的歧管$ m $上的粘性简化的bardina方程，该方程嵌入了$ \ mathbb {r}^3 $中。首先，我们证明了弱解决方案的存在和独特性，也证明了$ m $的全球吸引子的存在。然后，我们建立了吸引子的Hausdorff的上和下边界。我们还证明了在二维球上$ {s}^2 $上方程的惯性歧管的存在。
In this paper we study the viscous simplified Bardina equation on the two-dimensional closed manifold $M$ which is embedded in $\mathbb{R}^3$. First, we prove the existence and the uniqueness of the weak solutions and also the existence of the global attractor for the equation on $M$. Then we establish the upper and lower bounds of the Hausdorff and fractal dimensions of the attractor. We also prove the existence of an inertial manifold for the equation on the two-dimensional sphere ${S}^2$.
