The paper shows local well-posedness in electron MHD with partial resistivity, indicating progress in understanding this complex system.
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 21/2 2 1 2 D electron MHD with either horizontal or vertical resistivity and show local well-posedness in Sobolev spaces.
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Babaei et al. (2026) studied this question.
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