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

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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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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China

    Yongzhong Sun

  2. Academy of Mathematics and Systems Science, CAS, Beijing, 100190, People’s Republic of China

    Chao Wang

  3. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Zhifei Zhang

Authors
  1. Yongzhong Sun
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  2. Chao Wang
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  3. Zhifei Zhang
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Correspondence to Zhifei Zhang.

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Communicated by A. Bressan

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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

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