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甬江数学讲坛175讲(2021年第34讲)

发布日期:2021-07-05 文章来源:数学与统计学院

报告题目:Hydrodynamic limit for inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck/Navier-Stokes-Vlasov equations 报 告 人:姚磊(西北大学 教授) 报告时间:2021年7月6日 上午10:00开始 报告地点:龙赛理科楼北楼116会议室 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 Mellt-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 fluid density is bounded away from zero. 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等国际刊物发表学术论文40余篇。

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