讲座时间：4月23日周一下午14:30—15:30

讲座地点：南校3B207

讲座题目：Global well-posedness and large time behavior of classical solutions to the Vlasov-Fokker-Planck and Magnetohydrodynamics equations

报告人：蒋鹏副教授

 

内容简介：In this talk, we are concerned with the global well-posedness of the fluid-particle system which describe the evolutions of disperse two-phase flows. The system  consists of the Vlasov-Fokker-Planck equation for the dispersed phase (particles) coupled to the compressible magnetohydrodynamics equations modelling a dense phase (fluid) through the friction forcing. Global well-posedness of the Cauchy problem is established in perturbation framework, and rates of convergence of solutions toward equilibrium, which are algebraic in the whole space and exponential on torus, are also obtained under some additional conditions on initial data. The existence of global solution and decay rate of the solution are proved based on the classical energy estimates and Fourier multiplier technique, which are considerably complicated and some new ideas and techniques are thus required. Moreover, it is shown that neither shock waves nor vacuum and concentration in the solution are developed in a finite time although there is a complex interaction between particle and fluid.

 

蒋鹏副教授简介

蒋鹏，河海大学理学院、副教授，北京应用物理和计算数学研究所博士后，博士毕业于上海交通大学数学系，师从王亚光教授，曾访问过美国匹兹堡大学、宾夕法尼亚州立大学、 中科院数学所、明尼苏达大学、南京大学等。研究方向为偏微分方程。多篇论文发表在J. Differential Equations, Nonlinearity,   Discrete Contin. Dyn. Syst.,  J. Math. Anal. Appl.等国际知名SCI期刊。