On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations

Details On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations

2009-12-07

arxiv.org/abs/0912.1316v2

Mathematics

Analysis of PDEs

33 pages

Scientific paper

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei in [16] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier-Stokes equations. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the 3D inviscid model for a class of initial boundary value problems with smooth initial data of finite energy. We also prove the global regularity of the 3D inviscid model for a class of small smooth initial data.

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