On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler   Equations
  In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler's equations (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data. 
Kyudong Choi, Thomas Y. Hou, Alexander Kiselev, Guo Luo, Vladimir   Sverak, Yao Yao
math.AP