Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	李特，National University of Singapore
Inviter:	王益研究员
Title:	Nonlinear Stability of Shear Flows and Rotating Flows in Fluid Dynamics
Language:	Chinese
Time & Venue:	2023.01.03 10:00-11:00 腾讯会议：432-488-751
Abstract:	Hydrodynamic stability at high Reynolds number is a central topic in fluid mechanics. It is closely related to turbulence. Whereas the laminar velocity profile is linearly stable for all Reynolds number, Reynolds experiment reveals that laminar flows could be unstable and transit to turbulence at high Reynolds number. This phenomenon is described as subcritical transition. And the mechanism behind is not well understood yet. In order to investigate the dynamical nonlinear stability, we develop a systematic approach to establish sharp resolvent estimates for the linearized operator around certain typical shear flows and rotating flows. One of the main difficulties is that the linearized operator is non-self-adjoint and non-local such that the spectral analysis becomes very complicate. Based on the resolvent estimates, we first show the sharp enhanced-dissipation decay rate of the solution for the linearized system. We also derive the space-time estimates for the nonlinear part using the resolvent estimates. Combining all above, we obtain the nonlinear transition threshold for typical shear and rotating flows including Couette flow, Komolgorov flow, Oseen vortex, Taylor-Couette flow. This talk is based on a series of joint works by L.-D. Wei-Z. Zhang and by X. An-T. He-L..