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

2010/01/08 by Sun, Yongzhong, Wang, Chao, Zhang, Zhifei · 2 citations
#35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1001.1247

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 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.

Cited by

• Blow-up criterion for the compressible Navier--Stokes system with inflow-outflow boundary conditions
• Solvability of Euler equations in the fractional Sobolev spaces in a bounded smooth domain

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