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吕勇: Homogenization of compressible Navier-Stokes equations

时间:2020-12-17来源:数学学院

报告时间:2020年12月19日(星期六)14:00-15:00

报告地点翡翠湖校区科教楼B座1710室

吕勇 副教授

工作单位南京大学

举办单位:数学学院

报告简介

I will talk about the homogenization of compressible Navier-Stokes equations. Homogenization problems in fluid mechanics is the study of asymptotic behavior of fluid flows in domains perforated with a large number of tiny holes (obstacles).  For compressible Navier-Stokes equations, we show that when the holes are relatively small, the governed equation remain unchanged. The main difficulty lies in obtaining some uniform optimal high integrability of the fluid pressure, for which classicaly one uses the Bogovskii operator to obtain higher integrability.  Unfortunately, the norm of the classical Bogovskii opertor relaying on the Lipschitz norm of the domain. We constructed a Bogovskii type operator in perforated domains with a 'optimal' quantitative estimate with respect to the perforation parameter. In particular, this operator is uniformly bounded when in the case of small holes.

报告人简介

吕勇,南京大学数学系副教授。本科毕业于中国科技大学数学系,在法国巴黎七大取得硕士和博士学位,之后在布拉格查理大学从事博士后研究。研究领域为偏微分方程的数学分析,在非线性几何光学方程以及流体力学方程两个方向取得了突出的成绩。

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