Singularity formation to the 2D Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction

Abstract

The formation of singularity and breakdown of strong solutions to the two-dimensional (2D) Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction are considered. It is shown that for the initial density allowing vacuum, the strong solution exists globally if the density $\rho$ and the pressure $P$ satisfy $\Vert \rho {\Vert }_{L^{\infty }(0,T;L^{\infty })}+\Vert P{\Vert }_{L^{\infty }(0,T;L^{\infty })}<\infty$. In addition, the initial density can even have compact support. The logarithm-type estimate for the Lam{é} system and some weighted estimates play a crucial role in the proof.

arXiv comment15 pages

References in corpus (2)

• Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum
• Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of 2D Density-Dependent Navier-Stokes Equations with Vacuum

Cited by in corpus (3)

• Singularity formation to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain
• On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conduction
• Singularity formation to the Cauchy problem of the two-dimensional non-baratropic magnetohydrodynamic equations without heat conductivity