勷勤数学•专家报告

题      目：Stability and Large-Time Behavior of Navier-Stokes Equations with Anisotropic Dissipation

报  告  人：吴家宏 教授  (邀请人：李进开)

                                             University of Notre Dame

时      间：7月31日  15：00-16：00

地     点：华南师大第一课室大楼东102

报告人简介:

        Dr. Jiahong Wu is a Professor of Mathematics at the University of Notre Dame. His research focuses on the analysis and applications of fluid dynamics models, including the Navier-Stokes, the Boussinesq equations and magnetohydrodynamics (MHD) equations.

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.