On stability of steady circular flows in a two-dimensional exterior disk
On stability of steady circular flows in a two-dimensional exterior disk
复制标题
二维外圆盘内稳定循环流的稳定性
DOI：
10.1007/s00205-017-1105-4
复制
发表时间：
2017
影响因子：
2.5
通讯作者：
Y. Maekawa
中科院分区：
文献类型：
--
作者：
田丸博士;Masaru Ikehata;舟木直久;N. Bez and M. Sugimoto;Seiichi Kamada;Y. Maekawa
本文研究了二维Navier-Stokes方程在单位圆盘外区域上精确定常解的稳定性。这些静态解被称为旋转障碍物周围流动的简单模型，而由于它们以尺度临界顺序的空间衰减带来的困难，它们的稳定性一直是开放的。在本文中，我们肯定地解决这个问题的小的解决方案。也就是说，我们将证明，如果这些精确解足够小，那么它们是渐近稳定的smallL 2扰动。
We study the stability of some exact stationary solutions to the two-dimensional Navier–Stokes equations in an exterior domain to the unit disk. These stationary solutions are known as a simple model of the flow around a rotating obstacle, while their stability has been open due to the difficulty arising from their spatial decay in a scale-critical order. In this paper we affirmatively settle this problem for small solutions. That is, we will show that if these exact solutions are small enough then they are asymptotically stable with respect to smallL2perturbations.