Regularity of the $3D$ stationary Hall magnetohydrodynamic equations on   the plane
  We study the regularity of weak solutions to the 3D valued stationary Hall magnetohydrodynamic equations on $ \Bbb R^2$. We prove that every weak solution is smooth. Furthermore, we prove a Liouville type theorem for the Hall equations. 
Dongho Chae and Joerg Wolf
math.AP