The speaker: Xiao Ren (Fudan university, Shanghai, China)
Title of the talk: “Existence and uniqueness for plane stationary Navier–Stokes flows with compactly supported force”
Time: Thursday, 24 of February, 15:00 - 16:00
Abstract: We prove two basic estimates for 2D stationary Navier-Stokes solutions, which have rather simple forms. Then, we apply them to the stationary Navier–Stokes equations in the whole plane with an external force and with a prescribed constant spatial limit. Using the first estimate, we solve the key difficulties in applying Leray’s invading domains method in the whole plane and, as a consequence, prove the existence of stationary Navier-Stokes D-solutions with arbitrary compactly supported force. Using the second estimate, we verify the boundary condition at infinity in two different scenarios: (I) the limit velocity is sufficiently large with respect to the external force, (II) both the total integral of force and the limit velocity vanish. Hence, our method produces large class of new solutions with prescribed spatial limits. We also show the uniqueness of D-solutions to the forced problem in a perturbative regime.
The talk is based on the recent joint paper with Julien Guillod (Sorbonne Universite) and Mikhail Korobkov, see https://arxiv.org/abs/2111.11042
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
We sincerely hope you will be able to participate.
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.
2022-02-21