On Pseudospectral Bound for Non-selfadjoint Operators and Its Application to Stability of Kolmogorov Flows
On Pseudospectral Bound for Non-selfadjoint Operators and Its Application to Stability of Kolmogorov Flows
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DOI：
10.1007/s40818-019-0070-7
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发表时间：
2017-10
期刊：
影响因子：
2.8
通讯作者：
S. Ibrahim;Yasunori Maekawa;N. Masmoudi
中科院分区：
文献类型：
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作者：
S. Ibrahim;Yasunori Maekawa;N. Masmoudi
本文研究了二维Navier-Stokes方程在剪切外力作用下定常解Kolmogorov流的稳定性。当粘性系数足够小时，我们建立了线性稳定性估计，其中增强耗散在线性化问题的时间尺度上得到了严格的验证，该线性化问题的时间尺度已经得到了数值验证，并且比通常的粘性时间尺度短得多.我们的方法是基于对解决问题的详细分析。我们还提供了抽象的框架，这是适用于预解估计的Kolmogorov流。
We study the stability of the Kolmogorov flows which are stationary solutions to the two-dimensional Navier–Stokes equations in the presence of the shear external force. We establish the linear stability estimate when the viscosity coefficientis sufficiently small, where the enhanced dissipation is rigorously verified in the time scalefor solutions to the linearized problem, which has been numerically conjectured and is much shorter than the usual viscous time scale. Our approach is based on the detailed analysis for the resolvent problem. We also provide the abstract framework which is applicable to the resolvent estimate for the Kolmogorov flows.