A Blow-Up Criterion for the Compressible Navier-Stokes equations

Abstract

In this paper, we obtain a blow up criterion for strong solutions to the 3-D compressible Naveri-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. The key ingredients in our analysis are the a priori super-norm estimate of the momentum by a Moser-iteration and an estimate of the space-time square mean of the gradient of the density. In addition, initial vacuum is allowed in our case.

19 pages

References in corpus (2)

• A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations
• Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems

Cited by in corpus (3)

• A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations
• A Beale-Kato-Majda Blow-up criterion for the 3-D compressible Navier-Stokes equations
• Blow up criteria for the compressible Navier--Stokes equations