讲座题目：Stabilization and prevention of potential singularity formation

主办单位：三峡数学研究中心/三峡大学理学院

报告专家：吴家宏教授

报告时间： 2022年5月17日上午9:00-12:00

报告地点： 腾讯会议（ID:983 946 394）

专家简介：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，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重要贡献，先后在国际一流的学术刊物 (如：CPAM、CMP、ARMA、JFA、Adv. Math、SIAM、AIHP、CPDE、JDE) 发表学术论文140余篇. 论文引用次数高达4400多次.

报告摘要：This talk presents two examples of the smoothing and stabilizing phenomenon for coupled PDE systems that prevents potential finite-time singularity formation. The 3D incompressible Euler equation can potentially develop finite-time singularities, as indicated by recent numerical simulations and theoretical results. However, when the Euler equation is coupled with the equation of the non-Newtonian stress tensor via the Oldroyd-B model, small data global well-posedness can be established and the coupling prevents the potential singularity. The 3D anisotropic Navier-Stokes equation with dissipation in only one direction is not known to be globally well-posed. But, when coupled with the magnetic field via the magneto-hydrodynamic (MHD) system, we can show the global well-posedness near a background magnetic field. The magnetic field stabilizes the fluid.