主  讲  人：王术 教授（北京理工大学）
时      间：2015年12月2日 16:00—16:50
地      点：首都师大北二区教学楼 515 教室
主 办 单 位：必赢76net线路官网数学科学学院
内 容 介 绍：We study the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations. This 3D model is derived from the axisymmetric Navier-Stokes equations with swirl using a set of new variables. The model preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. We prove rigorously that the 3D model develops finite time singularities for a large class of initial data with finite energy and appropriate boundary conditions. Moreover, we also prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition. The related problems are surveyed and some recent results will also be reviewed.