English

Electroconvection in a Magnetic Field

Analysis of PDEs 2025-08-12 v1

Abstract

Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak solutions with LL^{\infty} data. We show that for strong enough magnetic fields, LL^{\infty}-small solutions are smooth globally in time and they obey surface quasigeostrophic equations in the limit of infinite magnetic field strength.

Keywords

Cite

@article{arxiv.2508.07439,
  title  = {Electroconvection in a Magnetic Field},
  author = {Elie Abdo and Peter Constantin and Mihaela Ignatova and Quyuan Lin},
  journal= {arXiv preprint arXiv:2508.07439},
  year   = {2025}
}
R2 v1 2026-07-01T04:43:17.278Z