On partial regularity for the steady Hall magnetohydrodynamics system

Abstract: We study partial regularity of suitable weak solutions of the steady Hall magnetohydrodynamics equations in a domain $\Omega \subset \Bbb R<sup>3$. 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 $\Omega=\Bbb R<sup>3$, we show that the set of possible singularities is compact.