  In the lubrication area, which is concerned with thin film flow, cavitation
has been considered as a fundamental element to correctly describe the
characteristics of lubricated mechanisms. Here, the well-posedness of a
cavitation model that can explain the interaction between viscous effects and
micro-bubbles of gas is studied. 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). This coupled
model seems never to be studied before from its mathematical aspects. Local
times existence results are proved and stability theorems are obtained based on
the continuity of the spectrum for bounded linear operators. Numerical results
are presented to illustrate these theoretical results.
