Blowup criteria for full compressible Navier-Stokes equations with vacuum state

Abstract

This paper deals with the global strong solution to the three-dimensional (3D) full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the temperature and some norm of the divergence of the velocity are bounded, for the global regularity of strong solution to the 3D compressible Navier-Stokes equations. This result indicates that the divergence of velocity fields plays a dominant role in the blowup mechanism for the full compressible Navier-Stokes equations in three dimensions.

Keywords

Compressible Navier-Stokes equations / Heat-conduction / Blowup criterion / Divergence of velocity

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