数学科学学院学术报告

--- 分析、偏微分方程与动力系统讨论班 (2025春季第11讲)

Stability and Large-Time Behavior of Compressible MHD Flows Near a Background Magnetic Field

吴家宏 (圣母大学)

时间：6月11日（周三）上午10:00-11:00

地点：沙河校区国实E806

摘要: Physical experiments and numerical simulations have revealed a remarkable stabilizing effect of magnetic fields: they can smooth and suppress instabilities in electrically conducting fluids. This phenomenon has motivated extensive research into the underlying mechanisms within the framework of the magnetohydrodynamics (MHD) equations. In this talk, I will present recent results on the nonlinear stability and long-time behavior of compressible MHD systems with anisotropic dissipation. In particular, I will discuss three settings: (1) the three-dimensional compressible non-resistive MHD equations near a background magnetic field satisfying a Diophantine condition; (2) the three-dimensional non-isentropic MHD equations with no velocity dissipation; and (3) the compressible MHD equations with horizontal magnetic diffusion near a general constant magnetic field. These results reveal a rich wave structure and uncover stabilizing mechanisms unique to compressible flows—phenomena that do not appear in the incompressible case.

报告人简介: 吴家宏教授1988年本科毕业于北京大学数学科学学院，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，现为美国圣母大学教授。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一系列重要贡献，在国际一流的学术刊I物CPAM、CMP、ARMA、Adv.Math、Math.Ann.、JFA、SIAM、AIHP、CPDE、JDE等发表学术论文180余篇。论文被国际同行引用超过6000次。

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邀请人：郑孝信、苑佳