Singularity formation to the Cauchy problem of the two-dimensional non-baratropic magnetohydrodynamic equations without heat conductivity

TL;DR

This paper investigates conditions under which strong solutions to 2D non-barotropic magnetohydrodynamic equations exist globally, showing that bounded density and pressure suffice, similar to the compressible Navier-Stokes case.

Contribution

It establishes a new global existence criterion for strong solutions of 2D non-barotropic MHD equations, independent of magnetic field effects.

Findings

Global existence when density and pressure are bounded

Criterion matches that of compressible Navier-Stokes equations

Method uses weighted energy estimates and Hardy-type inequality

Abstract

We study the singularity formation of strong solutions to the two-dimensional (2D) Cauchy problem of the non-baratropic compressible magnetohydrodynamic equations without heat conductivity. It is proved that the strong solution exists globally if the density and the pressure are bounded from above. In particular, the criterion is independent of the magnetic field and is just the same as that of the compressible Navier-Stokes equations. Our method relies on weighted energy estimates and a Hardy-type inequality.