On Partial Regularity for the Steady Hall Magnetohydrodynamics System.

We study partial regularity of suitable weak solutions of the steady Hall magnetohydrodynamics equations in a domain $${\Omega \subset \mathbb{R}^3}$$ . In particular, we prove that the set of possible singularities of the suitable weak solution has Hausdorff dimension at most one. Moreover, in the case $${\Omega=\mathbb{R}^3}$$ , we show that the set of possible singularities is compact. [ABSTRACT FROM AUTHOR]