Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping

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Abstract

In this paper, we establish a global existence (GE) result for the three‐dimensional compressible Euler equations (CEE) for generalized Chaplygin gas (GCG) with damping. More precisely, by transforming the three‐dimensional CEE for GCG with damping to a symmetric hyperbolic system, one shows that the total energy in H³ is strictly decaying with time for any sufficiently small initial data. As a result, the GE result follows from the local well‐posedness of the system in H³. This gives the first GE result relating to the three‐dimensional CEE. Copyright © 2020 John Wiley & Sons, Ltd.
Original languageEnglish
Pages (from-to)1176-1184
JournalMathematical Methods in the Applied Sciences
Volume44
Issue number2
Early online dateAug 2020
DOIs
Publication statusPublished - 30 Jan 2021

Citation

Cheung, K. L. (2021). Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping. Mathematical Methods in the Applied Sciences, 44(2), 1176-1184. doi: 10.1002/mma.6819

Keywords

  • Compressible Euler equations
  • Damping
  • Generalized Chaplygin gas
  • Global existence
  • Localwell-posedness

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