On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations
Abstract
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.
Keywords
Cite
@article{arxiv.0912.1316,
title = {On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations},
author = {Thomas Y. Hou and Zuoqiang Shi and Shu Wang},
journal= {arXiv preprint arXiv:0912.1316},
year = {2012}
}
Comments
33 pages