主讲人简介

李海梁，1999年于中国科学院数学研究所获得博士学位，偏微分方程专家，博士生导师。现任首都师范大学数学科学院院长，国家杰出青年科学基金获得者，新世纪百千万人才工程国家级人选。李海梁教授长期致力于非线性偏微分方程数学理论的研究，包括可压缩流体方程和Kinetic方程等，重点研究解的适定和性态分析等，取得了一系列有重要意义的创新成果，被国内外权威学术刊物(如Comm. Math. Phys., Arch. Ration. Mech. Anal., SIAM J.Math. Anal.,等)接受发表，对相关问题的研究产生了重要影响，受到国内外专家的好评。先后入选北京市“科技新星”计划（2005年）、教育部“新世纪优秀人才支持计划”（2007年）、人社部“国家百千万人才工程”（2015年）。荣获霍英东基金会“第十一届高校青年教师基金”资助（2008年）、北京市属高校人才强教深化计划“学术创新人才（2010年）”和“长城学者（2013年）”项目资助、以及国家自然科学基金委“杰出青年科学基金”项目资助（2012年）。

内容摘要

we investigate the wave phenomena to a fluid-particle model described by the multi-dimensional compressible Euler/Navier-Stokes coupled with the Vlasov-Fokker-Planck equation (Euler-VFP or NS-VFP) through the relaxation drag force on the fluid momentum equation and the Vlasov force on the particle transport. First, we prove the globally nonlinear time-asymptotical stability of the planar rarefaction wave to 3D Euler-VFP system, which as we know is the first result about the nonlinear stability of basic hyperbolic waves for the multi-dimensional compressible Euler equations with low order dissipative effects (i.e., relaxation friction damping). This new (hyperbolic) wave phenomena comes essentially from the fluid-particle interactions through the relaxation friction damping, which is different from the interesting diffusive phenomena for either the compressible Euler equations with damping  or the pure Fokker-Planck equation. Similar phenomena is also shown for 3D compressible NS-VFP,  and it is further proved that as the shear and bulk viscosities tend to zero, the global solution to 3D compressible NS-VFP system around the planar rarefaction wave converges to that of 3D Euler-VFP system at the uniform rate with respect to the viscosity coefficients. This is joint work with Teng Wang (BUT) and Yi Wang (AMSS) .

报告主持人

秦玉明 教授