Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations
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.
Submitted on 22 Jul 2014 (v1), last revised 20 Feb 2015 (this version, v2). The authors would like to thank Professors Russel Caflisch and Guo Luo for a number of stimulating discussions. We would also like to thank Professors Alexander Kiselev and Yao Yao for their interest in our work and for their valuable comments. The research was in part supported by NSF FRG Grant DMS-1159138.
Submitted - 1407.5740.pdf