Collisions and regularization for the 3-vortex problem
  We study the dynamics of 3 point-vortices on the plane for a fluid governed by Euler's equations, concentrating on the case when the moment of inertia is zero. We prove that the only motions that lead to total collisions are self-similar and that there are no binary collisions. Also, we give a regularization of the reduced system around collinear configurations (excluding binary collisions) which smoothes out the dynamics. 
Antonio Hern\'andez-Gardu\~no, Ernesto A. Lacomba