A Beale–Kato–Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows

摘要: We prove a blow-up criterion in terms of the upper bound (ρ, ρ−1, θ) for strong solution to three dimensional compressible viscous heat-conductive flows. The main ingredient proof is an priori estimate quantity independently introduced Haspot (Regularity weak solutions 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 effective flux.