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Multi-Fluid Models Including Compressible Fluids

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Didier Bresch

    (Université de Savoie Mont-Blanc, LAMA UMR 5127 CNRS Batiment le Chablais)

  • Benoît Desjardins

    (CMLA, ENS Cachan, CNRS and Modélisation Mesures et Applications S.A., Fondation Mathématique Jacques Hadamard)

  • Jean-Michel Ghidaglia

    (Ecole Normale Supérieure Paris-Saclay, Centre National de la Recherche Scientifique, Université Paris-Saclay, Centre de Mathématiques et de Leurs Applications (CMLA))

  • Emmanuel Grenier

    (Unité de Mathématiques Pures et Appliquées)

  • Matthieu Hillairet

    (Université de Montpellier, Institut Montpelliérain Alexander Grothendiek, UMR 5149 CNRS)

Abstract

In this chapter, we focus on multi-fluid models including compressible fluids in the isentropic or isothermal case. The main objective of these notes is to present at the level of beginners an introduction to mesoscopic multi-fluid models. The guideline is to show how we derive mathematically some multi-fluid systems starting from mono-fluid models and how we use the mathematical structures of multi-fluid PDEs to prove well-posedness (local strong and global weak solutions). We hope by this chapter to motivate young researchers to work on such a difficult topic important for applications in industry (turbulent mixing in nuclear industry, reactive flows, propulsion, sprays, …) and for environmental purposes (violent aerated flows, wave breaking, …) for which there exists few theoretical mathematical results.

Suggested Citation

  • Didier Bresch & Benoît Desjardins & Jean-Michel Ghidaglia & Emmanuel Grenier & Matthieu Hillairet, 2018. "Multi-Fluid Models Including Compressible Fluids," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 52, pages 2927-2978, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_74
    DOI: 10.1007/978-3-319-13344-7_74
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