BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Zhifei Zhang (Peking university) DTSTART:20200611T130000Z DTEND:20200611T135000Z DTSTAMP:20260423T035631Z UID:IMS/25 DESCRIPTION:Title: Tra nsition threshold for the 3D Couette flow in a finite channel\nby Zhif ei Zhang (Peking university) as part of PDE seminar via Zoom\n\n\nAbstract \nThe plane Couette flow is linearly stable for any Reynolds number. Howev er\, it could become nonlinearly unstable and transition to turbulence for small but finite perturbations at high Reynolds number. This is so-called Sommerfeld paradox. \nOne resolution of this paradox is to study the tran sition threshold problem\, which is concerned with how much disturbance wi ll lead to the instability of the flow and the dependence of disturbance o n the Reynolds number. In a joint work with Qi Chen and Dongyi Wei\, we sh owed that if the initial velocity $v_0$ satisfies $\\|v_0-(y\,0\,0)\\|_{H^ 2}\\le c_0{Re}^{-1}$ for some $c_0>0$ independent of $Re$\, then the solut ion of the 3D Navier-Stokes equations is global in time and does not trans ition away from the Couette flow in the $L^\\infty$ sense\, and rapidly co nverges to a streak solution for $t\\gtrsim Re^{1/3}$ due to the mixing-en hanced dissipation effect. This result confirms the transition threshold c onjecture proposed by Trefethen et al.(Science\, 261(1993)\, 578-584) for the 3D Couette flow in a finite channel with non-slip boundary condition.\ n\nHere is the poster of this talk:https://www.dropbox.com/s/gxyo8whzqnvco 3h/The%2010th%20PDE%20Seminar.png?dl=0\n\nPlease visit our website to get more information: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-vi a-zoom\n LOCATION:https://researchseminars.org/talk/IMS/25/ END:VEVENT END:VCALENDAR