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

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