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

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

2009-02-16

arxiv.org/abs/0902.2606v1

Physics

Mathematical Physics

19 pages

Scientific paper

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.

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