Well-posedness of the electron MHD with partial resistivity

Abstract

Due to the singular nonlinear Hall term, the non-resistive electron magnetohydrodynamics (MHD) is not known to be locally well-posed in general. In this paper we consider the $2\frac{1}{2}$D electron MHD with either horizontal or vertical resistivity and show local well-posedness in Sobolev spaces.