Refined blow-up criteria for the full compressible Navier–Stokes equations involving temperature

Abstract

In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier–Stokes equations, we improve almost all the blow-up criteria involving temperature to allow the temperature in its scaling invariant space for the 3D full compressible Navier–Stokes equations. Enlightening regular criteria via pressure \(\Pi =\frac{\text{ divdiv }}{-\Delta }(u_{i}u_{j})\) of the 3D incompressible Navier–Stokes equations on bounded domain, we generalize Beirao da Veiga’s result in (Chin Ann Math Ser B 16:407–412, 1995) from the incompressible Navier–Stokes equations to the isentropic compressible Navier–Stokes system in the case away from vacuum.

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Acknowledgements

The authors would like to express their deepest gratitude to the anonymous referee and the editors for carefully reading our manuscript whose invaluable comments and suggestions helped to improve the paper greatly. Jiu was partially supported by the National Natural Science Foundation of China (No. 11671273) and by Beijing Natural Science Foundation (No. 1192001). Wang was partially supported by the National Natural Science Foundation of China under grant (No. 11971446, No. 12071113 and No. 11601492). Ye was partially supported by the National Natural Science Foundation of China (No. 11701145 and No. 11971147) and Project funded by China Postdoctoral Science Foundation (No. 2020M672196).

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Correspondence to Yulin Ye.

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Jiu, Q., Wang, Y. & Ye, Y. Refined blow-up criteria for the full compressible Navier–Stokes equations involving temperature. J. Evol. Equ. (2021). https://doi.org/10.1007/s00028-020-00660-4

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Keywords

  • Full compressible Navier–Stokes equations
  • Strong solutions
  • Blow-up criteria

Mathematics Subject Classification

  • 35B65
  • 35D30
  • 76D05