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时jian:2020-12-17来源:shu学学院

报告时jian:2020nian12月19日(星期六)14:00-15:00

报告地点翡cuihu校区科教louBzuo1710shi

吕勇 副教授

gong作dan位nan京大学

举办dan位:shu学学院

报告简jie

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jie

吕勇,nan京大学shu学系副教授。本科毕业于zhongguo科技大学shu学系,zaifaguo巴li七大取得shuoshi和博shi学位,之后zai布拉ge查理大学磞ou虏﹕hi后研究。研究领域为pian微穤hi匠痰膕hu学分析,zaifei线xing几何光学方程以及流体力学方程两个方向取得了突出的cheng绩。

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