Note on Solution Regularity of the Generalized Magnetohydrodynamic Equations with Partial Dissipation

TL;DR

This paper investigates the regularity of solutions to n-dimensional magnetohydrodynamic equations with hyper-viscosity and zero resistivity, establishing conditions for global regularity.

Contribution

It proves global regularity of solutions under sufficiently strong hyper-viscosity in the generalized MHD equations with partial dissipation.

Findings

Global regularity achieved with strong hyper-viscosity

Conditions identified for solution smoothness

Extension of regularity results to n-dimensional case

Abstract

In this brief note we study the $n$-dimensional magnetohydrodynamic equations with hyper-viscosity and zero resistivity. We prove global regularity of solutions when the hyper-viscosity is sufficiently strong.