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We show that the viscous resistive magneto-hydrodynamics system with Halleffect is locally well-posed in $H^s(\mathbb R^n)\timesH^{s+1-\varepsilon}(\mathbb R^n)$ with $s>\frac{n}2-1$ and any small enough$\varepsilon>0$ such that $s+1-\varepsilon>\frac{n}2$. This space is to datethe largest local well-posedness space in the class of Sobolev spaces for thesystem. It is also optimal according to the predominant scalings of the twoequations in the system.

Local well-posedness for the Hall-MHD system in optimal Sobolev Spaces