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Global existence for the 2D Navier-Stokes flow in the exterior of a moving or rotating obstacle
Kinetic and Related Models ( IF 1 ) Pub Date : 2016-09-01 , DOI: 10.3934/krm.2016015
Shuguang Shao , Shu Wang , Wen-Qing Xu , Bin Han

We consider the global existence of the two-dimensional Navier-Stokes flow in the exterior of a moving or rotating obstacle. Bogovski$\check{i}$ operator on a subset of $\mathbb{R}^2$ is used in this paper. One important thing is to show that the solution of the equations does not blow up in finite time in the sense of some $L^2$ norm. We also obtain the global existence for the 2D Navier-Stokes equations with linearly growing initial velocity.

中文翻译:

2D Navier-Stokes 流在移动或旋转障碍物外部的全局存在性

我们考虑在移动或旋转障碍物外部二维纳维-斯托克斯流的全局存在。本文使用了 $\mathbb{R}^2$ 子集上的 Bogovski$\check{i}$ 运算符。一件重要的事情是证明方程的解在有限时间内不会在某些 $L^2$ 范数的意义上爆炸。我们还获得了初始速度线性增长的二维 Navier-Stokes 方程的全局存在性。
更新日期:2016-09-01
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