Magnetic Relaxation of a Voigt-MHD System

TL;DR

This paper constructs magnetohydrostatic solutions as limits of Voigt-approximated magnetohydrodynamics equations, demonstrating their regularity and nontriviality without artificial viscosity.

Contribution

It introduces a novel approach to obtain MHS solutions via Voigt approximations, avoiding artificial viscosity and establishing their regularity and nontriviality.

Findings

MHS solutions are regular and nontrivial.

Voigt approximations converge to MHS solutions.

Solutions are not Beltrami fields.

Abstract

We construct solutions of the magnetohydrostatic (MHS) equations in bounded domains and on the torus in three spatial dimensions, as infinite time limits of Voigt approximations of viscous, non-resistive incompressible magnetohydrodynamics equations. The Voigt approximations modify the time evolution without introducing artificial viscosity. We show that the obtained MHS solutions are regular, nontrivial, and are not Beltrami fields.