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Wave phenomena to three-dimensional fluid-particle model

时间:2020.11.1 10:00-11:30

地点:腾讯会议 777 403 242

主讲人:李海梁

主讲人简介:

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)。

活动内容摘要:

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) .

主持人:秦玉明