简介: |
Abstract: Abstract: In this talk, the singularity formation of a recently proposed 3D model for incompressible Euler and Navier-Stokes equations is discussed. This 3D model is derived from the axisymmetric Navier-Stokes equations with swirl using a set of new veriables. 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. Some numerical evidence supports that the 3D model may develop a potential finite time singularity. We will prove rigorously that the 3D model develops finite time singularities for a large class of initial data with finite energy and approriate boundary conditions. This work may shed interesting light into the stabilizing effect of convection for 3D incompressible Euler and Navier-Stokes equations. We also prove the global reguarity for a class of smooth initial data. |
