Regularity of the 3 D Stationary Hall Magnetohydrodynamic Equations on the Plane.

We study the regularity of weak solutions to the 3D valued stationary Hall magnetohydrodynamic equations on $${\mathbb{R}^2}$$ . We prove that every weak solution is smooth. Furthermore, we prove a Liouville type theorem for the Hall equations. [ABSTRACT FROM AUTHOR]