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

Thomas Y. Hou Caltech Zuoqiang Shi Tsinghua University Shu Wang Beijing University of Technology

Analysis of PDEs Numerical Analysis and Scientific Computing mathscidoc:1709.03001

Advances in Mathematics, 230, 607-641, 2012
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.
Finite time singularities; Nonlinear nonlocal system; Incompressible Navier–Stokes equations
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@inproceedings{thomas2012on,
  title={On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations},
  author={Thomas Y. Hou, Zuoqiang Shi, and Shu Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927153118437850837},
  booktitle={Advances in Mathematics},
  volume={230},
  pages={607-641},
  year={2012},
}
Thomas Y. Hou, Zuoqiang Shi, and Shu Wang. On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations. 2012. Vol. 230. In Advances in Mathematics. pp.607-641. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170927153118437850837.
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