About a cavitation model including bubbles in thin film lubrication taking convection into account

In lubrication problems, which concern thin film flow, cavitation has been considered as a fundamental element to correctly describe the characteristics of lubricated mechanisms. This cavitation model consists of a coupled problem between the compressible Reynolds PDE (that describes the flow) and the Rayleigh-Plesset ODE (that describes micro-bubbles evolution). Very few theoretical results exist in the mathematical literature about such couple problems. A complete form including bubbles convection is studied here. Local times existence results are proved based on the semi group theory. Stability theorems are obtained in a particular case.