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荔园学者Colloquium第八十二期

讲座题目: Resolvent Estimates for the Stokes Operator

主讲人：申仲伟 教授（美国肯塔基大学）

讲座时间：2024年5月31日上午10：30-11：30

讲座地点：十大正规平台官网粤海校区汇星楼一号教室    

内容概述：This talk is concerned with the study of resolvent estimates in L p for the Stokes operator. Such estimates play an essential role in the functional analytic approach of Fujita and Kato to the nonlinear Navier-Stokes equations in bounded domains. In the case of smooth domains (C 2 ), the resolvent estimate is well known and holds for all 1 < p < ∞. If the domain is Lipschitz, the estimate was established for a limited range of p, depending on the dimension, using the method of layer potentials and a real-variable argument. In this talk, I will discuss some recent work, joint with Jun Geng, for the case of C 1 domains. Starting with the upper half-space, using a perturbation argument, we are able to show that the resolvent estimate holds for all 1 < p < ∞. The case of exterior C 1 domains is also studied.

主讲人简介：Zhongwei Shen received his B.S. in mathematics from Peking University, M.S. from the Institute of Math of the Chinese Academy of Sciences, and his Ph.D. from the University of Chicago. He jointed the faculty at the University of Kentucky in 1995, where he was promoted to professor in 2003 and served as chair of the Math Department from 2007 to 2011. Shen’s research lies at the interface of harmonic analysis and partial differential equations. He is a member of the inaugural class of the American Math Society Fellow (2012) and a Simons Fellow (2021). In 2016 he was awarded the title of College of Arts and Sciences Distinguished Professor at the University of Kentucky.

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                                             数学科学学院

                                          2024年5月15日