Singularity formation to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain

Abstract

We consider the singularity formation of strong solutions to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain. It is shown that for the initial density allowing vacuum, the strong solution exists globally if the density and the pressure are bounded from above. Critical Sobolev inequalities of logarithmic type play a crucial role in the proof.

arXiv comment13 pages. arXiv admin note: substantial text overlap with arXiv:1801.10036, arXiv:1705.05161, arXiv:1705.06606

References in corpus (3)

• Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum
• Global Strong solution with vacuum to the 2D nonhomogeneous incompressible MHD system
• Singularity formation to the 2D Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction