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 $\Omega \subset {\mathbb{R}}^3$. 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.

23 pages(to appear in Communications in Mathematical Physics)

Cited by in corpus (3)

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• Existence, regularity and uniqueness of weak solutions with bounded magnetic fields to the steady Hall-MHD system
• On the regularity of magneto-vorticity field and the global existence for the Hall magnetohydrodynamic equations