主讲人：王术教授 （北京工业大学应用数理学院）

时  间：2014年 11月25日（周二）下午16:10-17:10

地  点：必赢76net线路官网北二区教学楼514

摘  要：We study the singularity formation and globalregularity 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.