Abstract
We prove a blow-up criterion in terms of the upper bound of (ρ, ρ −1, θ) for a strong solution to three dimensional compressible viscous heat-conductive flows. The main ingredient of the proof is an a priori estimate for a quantity independently introduced in Haspot (Regularity of weak solutions of the compressible isentropic Navier–Stokes equation, arXiv:1001.1581, 2010) and Sun et al. (J Math Pure Appl 95:36–47, 2011), whose divergence can be viewed as the effective viscous flux.
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Sun, Y., Wang, C. & Zhang, Z. A Beale–Kato–Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows. Arch Rational Mech Anal 201, 727–742 (2011). https://doi.org/10.1007/s00205-011-0407-1
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DOI: https://doi.org/10.1007/s00205-011-0407-1