Dissipative continuous Euler flows in two and three dimensions
  Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus $\mathbb T^3$. The building blocks in their proof are Beltrami flows, which are inherently three-dimensional. The purpose of this note is to show that the techniques can nevertheless be adapted to the two-dimensional case. 
Antoine Choffrut, Camillo De Lellis, and L\'aszl\'o Sz\'ekelyhidi Jr
math.AP