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

2018/09/29 by Xin Zhong, Zhong, Xin
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.01265

openalex publication_date 2018/09/29 · openalex created_date 2018/10/12 · openalex updated_date 2026/07/28

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.

Related

• Singularity formation to the 2D Cauchy problem of the full compressible Navier-Stokes equations with zero heat conduction
• A new blow-up criterion for the 2D full compressible Navier-Stokes equations without heat conduction in a bounded domain
• Singularity formation to the Cauchy problem of the two-dimensional non-baratropic magnetohydrodynamic equations without heat conductivity
• On Classical Solutions to the Cauchy Problem of the Two-Dimensional Barotropic Compressible Navier-Stokes Equations with Vacuum
• Global solutions of compressible Navier-Stokes equations with a density-dependent viscosity coefficient