Blow up for the 2D Euler Equation on Some Bounded Domains
  We find a smooth solution of the 2D Euler equation on a bounded domain which exists and is unique in a natural class locally in time, but blows up in finite time in the sense of its vorticity losing continuity. The domain's boundary is smooth except at two points, which are interior cusps. 
Alexander Kiselev, Andrej Zlatos
math.AP