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

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