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--- 分析与偏微分方程讨论班(2023春季第15讲)

Stabilizing phenomenon for electrically conducting fluids

吴家宏

(俄克拉荷马州立大学)

时间：7月7日（星期五）9:00-10:00

地点：腾讯会议： 535-821-655

https://meeting.tencent.com/dm/D2LMxKNgGibz

摘要:  Physical experiments have observed a remarkable stabilizing phenomenon: magnetic field can stabilize electrically conducting fluids. This talk presents two results that establish this observation as mathematically rigorous facts on the magnetohydrodynamic (MHD) equations. The first result is for a 3D incompressible MHD system with anisotropic dissipation. Without the magnetic field, the fluid is not known to be stable. But any perturbations near a suitable background magnetic field governed by this MHD system are shown to be asymptotically stable and decay algebraically in time. The second result concerns the 3D inviscid heat conductive compressible MHD system. Without the magnetic field, the fluid is governed by the 3D compressible Euler equations. Solutions of the compressible Euler equations can blow up in a finite time even when the initial data are smooth and small. However, this compressible MHD system is shown to be stable and decay near any background magnetic field satisfying a Diophantine condition.

报告人简介: 吴家宏教授1988年本科毕业于北京大学best365网页版登录，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，现为美国俄克拉荷马州立大学终身教授和杰出教授.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一系列重要贡献，先后在国际一流的学术刊物 CPAM、CMP、ARMA、JFA、Adv. Math、SIAM、AIHP、CPDE、JDE等发表学术论文140余篇. 论文被国际同行引用超过6000次。

邀请人： 郑孝信

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