报告题目：On an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations

报告人：王术

时间：2012年10月19日（星期五）10：00-11：00

地点：理科楼数学系A-304

摘要：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.

报告人简介：王术教授，北京工业大学数学一级学科博士点负责人，北京市重点建设学科“北京工业大学应用数学学科”学术负责人，2001年被评为中国科学院优秀博士后，2004年入选教育部新世纪优秀人才支持计划，2008年入选北京市属高校人才强教深化计划学术创新人才（拔尖人才），2011年入选北京工业大学“京华人才”。现为中国数学会理事，国家留学基金评审专家,北京工业大学应用数理学院副院长。

联系人：郑春雄