The speaker: Dr. Xiao Ren (Fudan University)
Title of the talk:“Leray's plane stationary solutions have the prescribed limit at infinity in the case of small Reynolds numbers”.
Time: Thursday, 13 of May 2021, 16:00 - 17:00.
Abstract. In the celebrated 1933 paper, J. Leray proposed the invading domains method to construct D-solutions for the stationary Navier-Stokes flow around obstacle problem. In two dimensions, whether Leray's D-solution achieves the prescribed limiting velocity at spatial infinity became a major open problem since then. In this paper, we solve this problem at small Reynolds numbers. The proof builds on a novel blow-down argument which rescales the invading domains to the unit disc, and the ideas developed in a recent paper [Korobkov-Pileckas-Russo2020], where the nontriviality of Leray solutions in the general case was proved, and [Korobkov-Ren-2021], where the uniqueness result for small Reynolds number was established. The talk is based on a joint work with M.Korobkov.
ZOOM Id: 836 7313 8944
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 Past Talks section.
Organizing Committee: Professors Zhen Lei, Mikhail Korobkov, Adele Ferone, Remigio Russo and Konstantin Pileckas.
This 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.