报告题目：Stability and Large-Time Behavior of Navier-Stokes Equations with Anisotropic Dissipation

报告人：吴家宏 教授  圣母大学

报告时间：2025-7-25（星期五）下午 16:00-18:00

报告地点：数信学院305

报告摘要：Navier-Stokes equations with anisotropic dissipation naturally arise in the modeling of various geophysical fluid flows. While global existence of small-data solutions to the three-dimensional incompressible Navier-Stokes equations with dissipation in only two directions has been well established, and results with sharp regularity have been obtained, the study of stability and long-time behavior is more recent and presents new difficulties. Classical tools, such as Schonbek’s Fourier splitting method, are no longer directly applicable in the anisotropic setting. Even in two dimensions, the stability and large-time behavior of solutions with anisotropic dissipation is not trivial. In this talk, I will present recent progress on the stability and long-time dynamics of incompressible Navier-Stokes flows with anisotropic dissipation and explain new techniques developed to overcome the difficulties introduced by the degeneracy.

报告人介绍：吴家宏教授1988年本科毕业于北京大学数学科学学院，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，现为美国圣母大学教授。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一系列重要贡献，在国际一流的学术刊物CPAM、CMP、ARMA、Adv.Math、Math.Ann.、JFA、SIAM、AIHP、CPDE、JDE等发表学术论文180余篇。论文被国际同行引用超过6000次。