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

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.

19 pages. arXiv admin note: substantial text overlap with arXiv:1705.05161, arXiv:1705.06606; text overlap with arXiv:1801.07589

References in corpus (4)

• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum
• Singularity formation to the 2D Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction
• On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conduction