Academic Communication

On an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations2015-12-02

Source: cnu       Clicks:       Size: small     middle       big

Speaker:Pro. Wang Shu 

Time:Dec 2, 2015 16:00—16:50

Loction:Room 517, Teaching Building, CNU Second North Campus

Organizer:School of Mathematical Sciences Capital Normal University

Introduction: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.