Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data

TL;DR

This paper proves the global existence of strong solutions for the planar non-resistive magnetohydrodynamic equations with large initial data, allowing vacuum and density discontinuities, by establishing new a priori estimates.

Contribution

It introduces the concept of a transverse effective viscous flux and proves global well-posedness under minimal initial density assumptions.

Findings

Global strong solutions exist for large initial data.

Vacuum and density discontinuities are permitted.

New a priori estimates are developed for the fluxes.

Abstract

In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of the proof is to establish the a priori estimates on the effective viscous flux and a newly introduced "transverse effective viscous flux" vector field inducted by the transverse magnetic field. The initial density is assumed only to be uniformly bounded and of finite mass and, in particular, the vacuum and discontinuities of the density are allowed.