报告题目：Hydrodynamic Limit for Inhomogeneous Incompressible Navier-Stokes-Vlasov-Fokker-Planck/Navier-Stokes-Vlasov Equations

主 讲 人：姚磊

单 位：西北大学

时 间：8月24日10:00

ZOOM ID：210 089 8623

密 码：123456

摘 要：

We study the hydrodynamic limit of the weak solutions to inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck equations in a two or three dimensional bounded domain. The proof relies on the relative entropy argument to obtain the strong convergences of the macroscopic density of the particles and fluid velocity, which extends the works of Goudon-Jabin-Vasseur[Indiana Univ. Math. J., 53(2004)] and Mellet-Vasseur [Comm. Math. Phys.,281(2008)] to inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck equations. At last, we give a recent result about the hydrodynamic limit for inhomogeneous incompressible Navier-Stokes-Vlasov equations in three dimensional periodic domain, under the assumption that the initial data is small in some sense and the initial density is bounded away from zero.

简 介：

姚磊，西北大学教授，博士生导师，2010年在华中师范大学获理学博士学位；曾获全国百篇优秀博士学位论文奖、陕西省杰出青年科学基金、陕西省青年科技新星。主要从事流体力学中的偏微分方程数学理论的研究，在Math. Ann.、JMPA、Ann. I. H. Poincaré-AN、SIAM JMA、JMFM、JDE等国际刊物发表学术论文40余篇。