题    目：Stabilizing phenomenon for incompressible fluids

主讲人：吴家宏 教授

单    位：美国圣母大学

时    间：2024年7月22日10：30

地    点：学院二楼会议室

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.

简    介：吴家宏教授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、美国俄克拉荷马州立大学，现为圣母大学教授。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重要贡献，先后在国际一流的学术刊物 (如：CPAM、CMP、ARMA、Adv. Math) 发表学术论文160余篇，科研成果被国际同行引用超过6000次。