Local well-posedness of the Hall-MHD system in $H^s({\mathbb{R}}^n)$ with $s>\frac{n}{2}$

Abstract

We establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space ${\left(H^s({\mathbb{R}}^n)\right)}^2$ with $s>\frac{n}{2}$. The previously known local well-posedness space was ${\left(H^s({\mathbb{R}}^n)\right)}^2$ with $s>\frac{n}{2}+1$. Thus the result presented here is an improvement.