On partial regularity for the $3D$ non-stationary Hall magnetohydrodynamics equations on the plane

We study partial regularity of weak solutions of the 3D valued non-stationary Hall magnetohydrodynamics equations on $ \Bbb R^2$. In particular we prove the existence of a weak solution whose set of possible singularities has the space-time Hausdorff dimension at most two.
Comment: 31 pages