Open Access

Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations

Contributed equally
Research in the Mathematical Sciences20152:5

https://doi.org/10.1186/s40687-015-0021-1

Received: 27 July 2014

Accepted: 13 February 2015

Published: 1 May 2015

Abstract

We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which approximates the dynamics of the Euler equations on the solid boundary of a cylindrical domain. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find are consistent with direct simulation of the model and enjoy some stability property.