Thomas Y. Hou, Zuoqiang Shi, Shu Wang
Published 2009-12-07, updated 2012-02-28Version 2
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.
Finite time singularity formation for moving interface Euler equations
Finite Time Blow-up of a 3D Model for Incompressible Euler Equations
Global Well-Posedness For Half-Wave Maps With $S^2$ and $\mathbb{H}^2$ Targets For Small Smooth Initial Data
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