信息公告
应用数理学院数学学科系列学术报告(4月26日)
发布时间:2019-04-12 

题目:Laplace and Stokes equations in a domain with a shrinking hole

报告人:Dr. Yong Lv, Professor(Nanjing University)

(吕勇,南京大学,博导,教授)

时间:2019年4月26日(周五)下午16:00-17:00

地点:应用数理学院应用数学研究所2315

摘要:In this talk, we consider the Dirichlet problem of the Laplace and Stokes equations in a domain with a shrinking hole in $R^d, \ d\geq 2$. A typical observation is that, the Lipschitz norm of the domain goes to infinity as the size of the hole goes to zero. Thus, if $p\neq 2$, the classical results indicate that the $W^{1,p}$ estimate of the solution may go to infinity as the size of the hole tends to zero. We give a complete description for the uniform $W^{1,p}$ estimates of the solution for all $1<p<\infty$. We show that the uniform $W^{1,p}$ estimate holds if and only if $d'<p<d$ ($p=2$ when $d=2$). This work is motivated by the study of homogenization problems in fluid mechanics, where there arises typically the Dirichlet problem of Stokes equations in a fixed domain with a small hole. Two applications in the study of homogenization problems in fluid mechanics are given: a generalization of the restriction operator and a construction of Bogovskii type operator in perforated domains with a quantitative estimate of the operator norm.

报告人简介:吕勇,教授,现在南京大学工作。本科毕业于中科大,在法国巴黎七大取得硕士和博士学位,之后在捷克首都布拉格查理大学从事博士后研究工作。主要研究领域是偏微分方程及其应用,侧重在几何光学以及流体力学。主要研究成果发表在Archive for Rational Mechanics and Analysis,Mémoires de la Société Mathématique de France,SIAM: Journal on Mathematical Analysis, Calculus of Variations and Partial Differential Equations,ESAIM: Control, Optimisation and Calculus of Variations,Journal of Differential Equations, Journal of Mathematical Fluid Mechanics等很具影响力的期刊上。

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联系人:王术、冯跃红

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