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 is motivated by a particular singularity formation scenario observed in numerical computation. 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 agree with direct simulation of the model and seem to have some stability. 
Thomas Y. Hou, Pengfei Liu
math.AP