Multi-fluid models including compressible fluids

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.