期刊
ADVANCES IN MATHEMATICS
卷 230, 期 2, 页码 607-641出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2012.02.015
关键词
Finite time singularities; Nonlinear nonlocal system; Incompressible Navier-Stokes equations
类别
资金
- NSF [DMS-0713670, DMS-0908546]
- China 973 Program [2011CB808002]
- PHR-IHLB [200906103]
- [NSFC 11071009]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0908546] Funding Source: National Science Foundation
We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] 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. (C) 2012 Elsevier Inc. All rights reserved.
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