題  目：Stabilizing phenomenon of fluids

内容簡介：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.

報告人：Jiahong Wu  Oklahoma State University

報告人簡介：吳家宏教授1988年本科畢業于北京大學數學科學學院，1996年在美國芝加哥大學獲得博士學位，師從世界著名數學家Peter Constantin院士。先後工作于美國普林斯頓高等研究院，美國德州大學奧斯汀分校，現為美國俄克拉荷馬州立大學終身教授和傑出教授。吳家宏教授長期緻力于非線性流體動力學方程的理論研究，在Navier-Stokes方程、準地轉方程、Boussinesq方程和MHD方程等數學前沿問題的研究上做出了一系列重要貢獻，先後在國際一流的學術刊物CPAM、CMP、ARMA、JFA、Adv. Math、SIAM、AIHP、CPDE、JDE等發表學術論文140餘篇。論文被國際同行引用超過6000次。

時  間：2023年6月27日（周二）下午 17：00 始

地  點：南海樓224室

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