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 $\Omega \subset \Bbb R^3$. 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 $\Omega=\Bbb R^3$, we show that the set of possible singularities is compact.