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

2009/12/07 by Thomas Y. Hou, Zuoqiang Shi, Hou, Thomas Y. +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0912.1316

Abstract

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

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