Blow up criteria for the compressible Navier--Stokes equations

Abstract

We study the strong solution to the 3-D compressible Navier--Stokes equations. We propose a new blow up criterion for barotropic gases in terms of the integral norm of density $\rho$ and the divergence of the velocity $\bu$ without any restriction on the physical viscosity constants. Our blow up criteria can be seen as a partial realization of the underlying principle that the higher integrability implies the boundedness and then eventual regularity. We also present similar blow up criterion for the heat conducting gases.

References in corpus (1)

• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations