On stability of physically reasonable solutions to the two-dimensional Navier-Stokes equations
On stability of physically reasonable solutions to the two-dimensional Navier-Stokes equations
复制标题
二维纳维-斯托克斯方程物理合理解的稳定性
DOI：
10.1017/s1474748019000240
复制
发表时间：
2021
影响因子：
0.9
通讯作者：
Y. Maekawa
中科院分区：
文献类型：
--
作者：
Y. Maekawa
经过障碍物的流动是流体力学的一个基本对象。 1967 年，芬恩和史密斯证明了当雷诺数足够小时，在二维外域建模此类流动时，纳维-斯托克斯方程存在平稳解（称为物理合理解）的唯一存在性。他们的解在空间无限处的渐近行为现已被详细研究并得到很好的理解，而由于二维特有的困难，其稳定性仍然是开放的。在本文中，我们证明芬恩和史密斯构造的物理合理解对于小的且局部化的初始扰动是渐近稳定的。
The flow past an obstacle is a fundamental object in fluid mechanics. In 1967 Finn and Smith proved the unique existence of stationary solutions, called the physically reasonable solutions, to the Navier–Stokes equations in a two-dimensional exterior domain modeling this type of flows when the Reynolds number is sufficiently small. The asymptotic behavior of their solution at spatial infinity has been studied in detail and well understood by now, while its stability has remained open due to the difficulty specific to the two-dimensionality. In this paper, we prove that the physically reasonable solutions constructed by Finn and Smith are asymptotically stable with respect to small and well-localized initial perturbations.