Transition Threshold for the 2-D Couette Flow in a Finite Channel
Transition Threshold for the 2-D Couette Flow in a Finite Channel
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DOI：
10.1007/s00205-020-01538-y
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发表时间：
2020-05
影响因子：
2.5
通讯作者：
Qi Chen;Te Li;Dongyi Wei;Zhifei Zhang
中科院分区：
文献类型：
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作者：
Qi Chen;Te Li;Dongyi Wei;Zhifei Zhang
本文研究了有限通道中高Reynolds数Rein条件下Couette流（y，0）的二维Navier-Stokes方程的转捩阈值问题。我们发展了一个系统的方法来建立线性化算子的预解估计和线性化Navier-Stokes方程的时空估计。特别是，三种重要的影响-增强耗散，无粘阻尼和边界层-被集成到一个尖锐的形式的时空估计。作为应用，我们证明了：如果初始速度满足对某个与Re无关的小c，则二维Navier-Stokes方程的解在任意时刻保持在Couette流的内。
In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations around the Couette flow (y, 0) at high Reynolds numberRein a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier–Stokes equations. In particular, three kinds of important effects—enhanced dissipation, inviscid damping and a boundary layer–are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocitysatisfiesfor some smallcindependent ofRe, then the solution of the 2-D Navier–Stokes equations remains withinof the Couette flow for any time.