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  • Research Article
  • 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:

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.

Keywords

  • Euler Equation
  • Singular Solution
  • Interval Arithmetic
  • Decay Condition
  • Local Truncation Error

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