The speaker: Professor Chunjing Xie (Shanghai Jiao Tong University, China).
Title of the talk: "The uniqueness and existence of steady solutions of incompressible Navier-Stokes system in a nozzle".
Time: Thursday, 14 of December 2023, 15:00 - 16:00.
Abstract: A longstanding open problem for steady incompressible Navier-Stokes is the so called the Leray problem, which aims to give the existence of steady flows in an infinitely long nozzle with Poiseuille flows as far field behavior. The problem was solved by Amick, Ladyzhenskaya, Solonnikov, etc when the fluxes of the flows are small. When the flux is large, the existence of solutions to steady Navier-Stokes system was obtained by Ladyzhenskaya and Solonnikov. In order to completely solve the Leray problem, we may need to prove global uniqueness of Poiseuille flows in a straight cylinder. In this talk, we first address the recent progress on nonlinear structural stability of Hagen-Poiseuille flows in a pipe, in particular, the uniform stability of these flows with respect to the mass flux, where the key ingrident is the analysis of the associated linearized problem. Second, we prove the existence of the solutions in a channel when the flows satisfy the Navier boundary conditions where the uniform local estimates play a crucail role.
ZOOM link: https://us02web.zoom.us/j/83673138944?pwd=azQyc1BwUjJFY3VjMStLbFR5Z2VwUT09
ZOOM Id: 836 7313 8944
Passcode: 808818
We are pleased to inform you that the information on previous talks is available on the seminar web page
https://researchseminars.org/seminar/Cafe_Analysis_and_Fluid
see PastTalks section
Organizing Committee: Professors Zhen Lei, Mikhail Korobkov,
Adele Ferone, Remigio Russo, and Konstantin Pileckas
The seminar is organized by Fudan University (Shanghai, China) with the collaboration of Universita degli studi della Campania "Luigi Vanvitelli" (Caserta, Italy) and Vilnius University (Vilnius, Lithuania). This seminar is meant to gather renowned experts working on Geometric and Real Analysis with applications to PDEs and Mathematical Physics and represents an opportunity for presenting high-impact research, as well as facilitating the exchange of ideas between researchers.
2023-12-08