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

By Yongzhong Sun, Chao Wang, Zhifei Zhang. 2010

244 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ea152749ffdaa5ba72a6d638ac4ac9ee3dcf506c

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

A Beale–Kato–Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows (2011, methodology): “([24]) Let be a bounded Lipschitz domain in R3 and f ∈ W 1,q( ) with q ∈ (3,∞).”
Relative Entropies, Suitable Weak Solutions, and Weak-Strong Uniqueness for the Compressible Navier–Stokes System (2011, background): “[23] Y. Sun, C. Wang, and Z. Zhang.”
Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows (2012, background): “Then, to overcome the difficulty caused by the boundary when is bounded, motivated by [9,36], we decompose the velocity into two parts (see (3.”
ON THE ILL-POSEDNESS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS (2011, background): “dely open, even in two dimensional case. For the initial density with compact support, Xin [18] proved that any non-zero smooth solutions of (1.2) will blow up in ﬁnite time. Recently, Sun-Wang-Zhang [16, 17] showed that smooth solution will not blow up as long as the upper bound of the density( and”