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
JournalMathematical Methods in the Applied Sciences
Early online dateAug 2020
DOIs
Publication statusE-pub ahead of print - Aug 2020

Citation

Cheung, K. L. (2020). Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping. Mathematical Methods in the Applied Sciences. Advance online publication. doi: 10.1002/mma.6819

Keywords

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

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