Strong solutions to the Cauchy problem of the two-dimensional non-baratropic non-resistive magnetohydrodynamic equations with zero heat conduction

TL;DR

This paper proves the local existence of strong solutions to the 2D non-barotropic, non-resistive MHD equations with zero heat conduction under certain initial decay conditions, using weighted energy estimates.

Contribution

It establishes the existence of local strong solutions for the 2D non-resistive, non-barotropic MHD equations with vacuum, under specific initial decay assumptions.

Findings

Existence of local strong solutions under initial decay conditions.

Use of weighted energy estimates to handle vacuum and decay.

Results applicable to the whole 2D space with zero heat conduction.

Abstract

This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy estimates, we prove that there exists a local strong solution provided the initial density and the initial magnetic decay not too slow at infinity.