学术报告：Hydrodynamic limit for inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck/Navier-Stokes-Vlasov equations
发布时间：2021-07-06 浏览次数：281
报告人：姚磊
报告时间：2021年7月9日上午8:30-10:00
报告地点：育才理科综合楼103
报告题目：Hydrodynamic limit for inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck/Navier-Stokes-Vlasov equations
报告人简介：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等期刊发表学术论文40余篇。
报告摘要: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.