报告名称：The MHD equations of damped wave type in Sobolev space

报告时间：2023年6月27日上午10：00--11:00

报告地点：龙洞校区行政楼610房间

报 告 人：吴家宏教授

邀 请 人：翟小平

报告摘要：The magnetohydrodynamic system of damped wave type (abbreviated as MHD-wave system) is formally derived from Maxwell’s equations of electromagnetism by keeping the usually ignored small term involving the product of permittivity and magnetic permeability. This extra term in the MHD-wave system assumes the form $\gamma \partial_{tt} b$ with $\gamma>0$ being a small constant and $b$ the magnetic field. Mathematically this term makes the global well-posedness problem much more challenging than the corresponding MHD system. Even the global existence and regularity problem for the 2D MHD-wave system appears to be open. This talk presents a recent global well-posedness result in a critical Sobolev setting when $\gamma$ and the size of the initial data satisfy a suitable constraint. In addition, the solution of the MHD-wave system is shown to converge to that of the corresponding MHD system with an explicit rate. The energy method does not work here and this result presents a new approach.

报告人简介：吴家宏教授本科毕业于北京大学，1996年在美国芝加哥大学获得博士学位，师从世界著名数学家Peter Constantin院士. 先后工作于美国普林斯顿高等研究院，美国德州大学奥斯汀分校，美国俄克拉荷马州立大学，现为圣母大学杰出教授。吴家宏教授长期致力于非线性流体动力学方程的理论研究，在Navier-Stokes方程、准地转方程、Boussinesq方程和MHD方程等数学前沿问题的研究上做出了重要贡献，先后在国际一流的学术刊物 (如：CPAM、CMP、ARMA、JFA、Adv. Math、SIAM、AIHP、CPDE、JDE) 发表学术论文140余篇. 科研成果被国际同行引用超过6000次，是这一领域杰出的华人数学家。