Reduced models for electron magnetohydrodynamics: well-posedness and singularity formation

TL;DR

This paper introduces simplified one-dimensional models for 3D electron magnetohydrodynamics, demonstrating conditions for well-posedness and potential for finite-time singularity formation due to nonlocal nonlinear effects.

Contribution

It develops new reduced models capturing key nonlinear and nonlocal features of electron MHD, analyzing their well-posedness and singularity behavior.

Findings

Local well-posedness under certain conditions

Finite-time singularity possible with nonlocal transport

Models reveal complex nonlinear dynamics in electron MHD

Abstract

We propose some one-dimensional reduced models for the three-dimensional electron magnetohydrodynamics which involves a highly nonlinear Hall term with intricate structure. The models contain nonlocal nonlinear terms. Local well-posedness is obtained in certain circumstances. In contrast, for a model with nonlocal transport term, we show that finite time singularity may occur for some initial data.