报告人：王益（中国科学院数学与系统科学研究院）

邀请人：雷远杰

报告时间：2021年1月26日（星期二）10:00-12:00

报告地点：腾讯会议 ID：164 421 407

报告题目：Wave phenomena to three-dimensional fluid-particle model

报告摘要：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.

报告人简介：王益，国家高层次青年人才，博士毕业于中国科学院数学与系统科学研究院，同年留院工作，现为中国科学院数学与系统科学研究院研究员，博士生导师。主要从事非线性偏微分方程的数学分析研究，如可压缩Navier-Stokes方程、Boltzmann方程的解的整体适定性，包括非线性双曲波的稳定性、粘性极限以及流体动力学极限等。