Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure

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Abstract

We obtain some refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure. For the Cauchy problem of the 3-D compressible Navier–Stokes system with potential force term and general pressure, the strong solution exists globally if the velocity satisfies the Serrin’s condition and the sup-norm of the density is bounded. On the other hand, for the case without initial vacuum state, the blow-up criterion can be shown to be depending on density only. The proof is based on some new a priori estimates for 3-D compressible Navier–Stokes equations coupled with steady state solutions. Copyright © 2021 The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Original languageEnglish
Article number18
JournalZeitschrift für angewandte Mathematik und Physik
Volume73
Issue number1
Early online date02 Dec 2021
DOIs
Publication statusE-pub ahead of print - 02 Dec 2021

Citation

Suen, A. (2022). Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure. Zeitschrift für angewandte Mathematik und Physik, 73(1). Retrieved from https://doi.org/10.1007/s00033-021-01652-1

Keywords

  • Navier–Stokes equations
  • Compressible flow
  • Potential force
  • Blow-up criteria

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