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

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

2010-01-08

arxiv.org/abs/1001.1247v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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