Stabilizing phenomenon for incompressible fluids.

報告題目：Stabilizing phenomenon for incompressible fluids.

報 告 人：Wu Jiahong 教授 圣母大學

邀請人：王裴昕

報告時間：2024年6月17日（周一） 9：00-10：00（北京時間）

報告地點：南校區(qū)會議中心103報告廳

報告人簡介：吳家宏教授1988年本科畢業(yè)于北京大學，1996年在美國芝加哥大學獲得博士學位，師從世界著名數(shù)學家Peter Constantin院士。 先后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，俄克拉荷馬州立大學，現(xiàn)為美國圣母大學教授.

報告摘要:

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.

主辦單位：數(shù)學與統(tǒng)計學院