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arXiv · 1203.5151

Finite Time Blow-up of a 3D Model for Incompressible Euler Equations

Thomas Y. Hou·Zhen Lei
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Abstract

We investigate the role of convection on its large time behavior of 3D incompressible Euler equations. In \cite{HL09a}, we constructed a new 3D model by neglecting the convection term from the reformulated axisymmetric Navier-Stokes equations. This model preserves almost all the properties of the full Navier-Stokes equations, including an energy identity for smooth solutions. The numerical evidence presented in \cite{HL09a} seems to support that the 3D model may develop a finite time singularity. In this paper, we prove rigorously that the 3D inviscid model develops a finite time singularity for a family of smooth initial data whose energy is finite and conserved in time.

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Thomas Y. Hou, Zhen Lei. 2012-04-17. Finite Time Blow-up of a 3D Model for Incompressible Euler Equations. https://arxiv.org/abs/1203.5151

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