Dissipation wavenumber and regularity for electron magnetohydrodynamics

TL;DR

This paper investigates the dissipation mechanisms in electron magnetohydrodynamics (MHD), establishing a determining wavenumber and regularity conditions that challenge previous numerical findings of no dissipation cutoff.

Contribution

It introduces a theoretical framework for dissipation wavenumber and regularity in electron MHD, providing analytical results that question prior numerical conclusions.

Findings

Existence of determining wavenumber for electron MHD

Regularity condition based on low modes of the solution

Challenges previous numerical evidence of no dissipation cutoff

Abstract

We consider the electron magnetohydrodynamics (MHD) with static background ion flow. A special situation of $B(x,y,t)=\nabla\times (a\vec e_z)+b \vec e_z$ with scalar-valued functions $a(x,y,t)$ and $b(x,y,t)$ was studied numerically in the physics paper [7]. The authors concluded from numerical simulations that there is no evidence of dissipation cutoff for the electron MHD. In this paper we show the existence of determining wavenumber for the electron MHD, and establish a regularity condition only on the low modes of the solution. Our results suggest that the conclusion of the physics paper on the dissipation cutoff for the electron MHD is debatable.