Stability and instability of the 3D incompressible viscous flow in a bounded domain
Stability and instability of the 3D incompressible viscous flow in a bounded domain
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DOI：
10.1007/s00526-022-02205-8
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发表时间：
2022-03
影响因子：
2.1
通讯作者：
Fucai Li;R. Pan;Zhipeng Zhang
中科院分区：
文献类型：
--
作者：
Fucai Li;R. Pan;Zhipeng Zhang
本文研究了速度满足Navier边界条件的有界单连通区域内三维均匀不可压缩粘性流动定态(为常数)的稳定性和不稳定性。结果表明，存在一个临界滑移长度，其中存在一个仅依赖于区域的显式通用常数和粘性系数，使得当滑移长度小于临界滑移长度时，稳态是线性和非线性不稳定的，反之，稳态是线性和非线性稳定的。
In this paper, we investigate the stability and instability of the steady state(is a constant) for the 3D homogeneous incompressible viscous flow in a bounded simply connected domain with a smooth boundary where the velocity satisfies the Navier boundary conditions. It is shown that there exists a critical slip length, whereis an explicit generic constant depending only on the domain (given in ) andis the viscosity coefficient, such that when the slip lengthis less than, the steady stateis linearly and nonlinearly unstable; and conversely, the steady stateis linearly and nonlinearly stable when.