Local well-posedness of the Hall-MHD system in $H^s(\mathbb {R}^n)$ with $s>\frac n2$

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 $s>\frac n2$. The previously known local well-posedness space was $\left(H^s(\mathbb{R}^n)\right)^2$ with $s>\frac n2+1$. Thus the result presented here is an improvement.