On the stability threshold for rotating fluids near Couette flow
报告人：许孝精 (北京师范大学)
时间：2026-01-04 16:00-17:00
地点：智华楼王选报告厅
Abstract: In this talk, I shall introduce some results on the nonlinear stability for the incompressible rotating fluids in T×R×T near the Couette flow, by precisely quantifying the stability threshold at high Reynolds number. For the Navier-Stokes equations with rotation, we establish the nonlinear stability in the so-called Bradshaw Richardson stable regime \beta(\beta-1)>0 for initial velocity perturbations of size O(\nu) in H^{\sigma} with \sigma>9/2. For the rotating Boussinesq equations, we analyze the coupled system of the Couette flow and a stable temperature stratification 1+az (a>0). Nonlinear stability is also constructed, showing that the solutions do not transition away from the steady state, provided the initial perturbations of size O(\nu^{14/15}) . This talk is based on joint work with Wenting Huang (BNU), Zekai Luo (BNU) and Ying Sun (BUPT).
