题  目：Stabilizing phenomenon of fluids

内容简介：This talk presents several examples of a remarkable stabilizing phenomenon.  The results of T. Elgindi and T. Hou's group show that the 3D incompressible Euler equation can blow up in a finite time. Even small data would not help. But when the 3D Euler is coupled with the non-Newtonian stress tensor in the Oldroyd-B model, small smooth data always lead to global and stable solutions.The 3D incompressible Navier-Stokes equation with dissipation in only one direction is not known to always have global solutions even when the initial data are small. However, when this Navier-Stokes is coupled with the magnetic field in the magneto-hydrodynamic system, solutions near a background magnetic field are shown to be always global in time. The magnetic field stabilizes the fluid. Solutions of the compressible Euler equations can blow up in a finite time even when the initial data are smooth and small. But the 3D inviscid heat conductive compressible MHD system is shown to be stable and decay near any background magnetic field satisfying a Diophantine condition. In all these examples the systems governing the perturbations can be converted to damped wave equations, which reveal the smoothing and stabilizing effect.

报告人：Jiahong Wu  Oklahoma State University

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。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。

时  间：2023年6月27日（周二）下午 17：00 始

地  点：南海楼224室

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2023年6月25日