Speaker: Xu Xiaojing, professor and doctoral supervisor, Beijing Normal University

Date: July 14, 2025

Time: 15:30-16:30 pm

Location: B1032, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

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 Re: Our aim is to determine the stability threshold index on 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_in‖H^σ< δRe^-1for any σ > 9/2 and some δ = δ(σ) > 0, 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.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/204393.htm