“数理论坛”第106期：From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law

报告题目

From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law

报告时间

2019年9月12日（周四）,上午10:00—11:00

报告地点

东区教学综合楼A1404室

报告人

罗益龙 博士

报告人

简介

罗益龙博士，香港城市大学博士后。2017年于中科院数学与系统科学研究院取得博士学位，指导老师为李嘉禹教授与江宁教授，随后在武汉大学数学与统计学院进行博士后研究。主要从事流体动力学、分子动理学奇异极限、以及双曲型液晶等复杂流体模型，已在国际SCI学术杂志如SIAM-JMA、JDE、CMS等发表论文数篇。

报告摘要

For the two-species Vlasov-Maxwell-Boltzmann (VMB) system with the scaling under which the moments of the fluctuations to the global Maxwellians formally converge to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) system with Ohm's law, we prove the uniform estimates with respect to Knudsen number $\eps$ for the fluctuations. As consequences, the existence of the global in time classical solutions of VMB is established. Furthermore, the convergence of the fluctuations of the solutions of VMB to the classical solutions of NSFM with Ohm's law is rigorously justified.

This limit was justified in the recent breakthrough of Arsenio and Saint-Raymondfrom renormalized solutions of VMB to dissipative solutions of incompressible viscous electro-magneto-hydrodynamics under the corresponding scaling. In this sense, our result gives a classical solution analogue of the corresponding limit in Arsenio and Saint-Raymond's work.

邀请人

张腾飞 特任副教授

2019年9月10日