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Serrin-Type Blowup Criterion for Full Compressible Navier–Stokes System

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Abstract

The authors establish a Serrin-type blowup criterion for the Cauchy problem of the three-dimensional full compressible Navier–Stokes system, which states that a strong or smooth solution exists globally, provided that the velocity satisfies Serrin’s condition and that the temporal integral of the maximum norm of the divergence of the velocity is bounded. In particular, this criterion extends the well-known Serrin’s blowup criterion for the three-dimensional incompressible Navier–Stokes equations to the three-dimensional full compressible system and is just the same as that of the barotropic case.

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Authors and Affiliations

  1. NCMIS, AMSS, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Xiangdi Huang

  2. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 560-0043, Toyonaka, Osaka, Japan

    Xiangdi Huang

  3. Institute of Applied Mathematics & NCMIS, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Jing Li

  4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Yong Wang

Authors
  1. Xiangdi Huang
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  2. Jing Li
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  3. Yong Wang
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Corresponding author

Correspondence to Jing Li.

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Communicated by P.-L. Lions

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Huang, X., Li, J. & Wang, Y. Serrin-Type Blowup Criterion for Full Compressible Navier–Stokes System. Arch Rational Mech Anal 207, 303–316 (2013). https://doi.org/10.1007/s00205-012-0577-5

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  • DOI: https://doi.org/10.1007/s00205-012-0577-5

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