A Beale-Kato-Majda Blow-up criterion for the 3-D compressible Navier-Stokes equations

Abstract

We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to the 3-D compressible Navier-Stokes equations. The initial vacuum is allowed. The main ingredient of the proof is \textit{a priori} estimate for an important quantity under the assumption that the density is upper bounded, whose divergence can be viewed as the effective viscous flux.

17 pages

References in corpus (2)

• A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations
• A Blow-Up Criterion for the Compressible Navier-Stokes equations

Cited by in corpus (4)

• Blow up criterion for compressible nematic liquid crystal flows in dimension three
• Serrin Type Criterion for the Three-Dimensional Viscous Compressible Flows
• A blow-up criterion for compressible viscous heat-conductive flows
• A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with Vacuum