报告题目：On the Sobolev stability threshold for 3D Navier-Stokes equations with rotation near the Couette flow

报告人：许孝精教授(北京师范大学)

报告时间：2026年6月16日上午9点30 分-10点30分

报告地点：数135

报告摘要：In this talk, we investigate the dynamic stability of periodic, plane Couette flow in the three-dimensional Navier-Stokes equations with rotation at high Reynolds number $\mathbf{Re}$. Our aim is to determine the stability threshold index on $\mathbf{Re}$: the maximum range of perturbations within which the solution remains stable. Initially, we examine the linear stability effects of a linearized perturbed system. Comparing our results with those obtained by Bedrossian, Germain, and Masmoudi [Ann. Math. 185(2): 541–608 (2017)], we observe that mixing effects (which correspond to enhanced dissipation and inviscid damping) arise from Couette flow while Coriolis force acts as a restoring force inducing a dispersion mechanism for inertial waves that cancels out lift-up effects occurred at zero frequency velocity. This dispersion mechanism exhibits favorable algebraic decay properties distinct from those observed in classical 3D Navier-Stokes equations. Consequently, we demonstrate that if initial data satisfies $\|u_{\mathrm{in}}\|_{H^{\sigma}}<\delta \mathbf{Re}^{-1}$ for any $\sigma>\frac{9}{2}$ and some $\delta= \delta(\sigma) >0$ depending only on $\sigma$, then the solution to the 3D Navier-Stokes equations with rotation is global in time without transitioning away from Couette flow. This is a joint work with Wenting Huang and Ying Sun.

报告人简介：许孝精，北京师范大学学数学科学学院教授，“京师学者”特聘教授，博士生导师。主要研究来自流体动力学中的偏微分方程组的数学理论，主持多项国家自然科学基金项目和省部级科研项目，在不可压缩流体力学的数学理论研究中取得系列重要进展，发表在JMPA、SJMA、JNLS、JDE、Nonlinearity等国际期刊上。曾多次访问法国、美国、加拿大、波兰和香港等地知名高校，进行科研合作。