报告题目：Stabilizing phenomenon for incompressible fluids.

报 告 人：Wu Jiahong 教授 圣母大学

邀请人：王裴昕

报告时间：2024年6月17日（周一） 9：00-10：00（北京时间）

报告地点：南校区会议中心103报告厅

报告人简介：吴家宏教授1988年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，俄克拉荷马州立大学，现为美国圣母大学教授.

报告摘要:

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 2D Navier-Stokes in R^2 with dissipation in only one direction are not known to be stable, but the Boussinesq system involving this Navier-Stokes is always stable near the hydrostatic equilibrium. The buoyancy forcing helps stabilize the fluid. In all these examples the systems governing the perturbations can be converted to damped wave equations, which reveal the smoothing and stabilizing effect.

主办单位：best365亚洲版登录