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arXiv:1203.5151 [math.AP]AbstractReferencesReviewsResources

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

Thomas Y. Hou, Zhen Lei

Published 2012-03-23, updated 2012-04-17Version 2

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.

Comments: This paper has been withdrawn by the author. We are not able to construct data which meets the requirements in the main Theorem at this moment
Categories: math.AP
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