Blowup for the forced electron MHD
Analysis of PDEs
2025-03-20 v1
Abstract
The electron magnetohydrodynamics (MHD) contains a highly nonlinear Hall term with an interesting structure. Exploring the Hall nonlinear structure, we investigate possible phenomena of finite time blow up for the electron MHD with a (non-rough) forcing. When the magnetic field has zero horizontal components, the vertical component equation has a mixing feature with the mixer being the current flow. By constructing a magnetic field profile whose current density is approximately a hyperbolic flow near the origin, we show blowup develops in finite time. In another setting when the magnetic field is a shear type, the Hall term vanishes, and finite time blowup can be obtained for the forced electron MHD as well.
Cite
@article{arxiv.2503.14777,
title = {Blowup for the forced electron MHD},
author = {Mimi Dai},
journal= {arXiv preprint arXiv:2503.14777},
year = {2025}
}