A new cavitation model in lubrication: the case of two-zone cavitation

A generalization of the Elrod-Adams model of cavitation in lubricated devices is proposed, such that the translation velocity for the saturation field can be given any value between and , with being the relative speed of the surfaces. The lack of uniqueness of the classical model when is explained and a suitable supplementary condition is proposed to fix this issue. The new model is rigorously analyzed, though in the simplified mathematical setting of a one-dimensional problem with a single pressurized region. The main result states the existence of a unique solution globally in time, unless of course the cavitation boundary leaves the domain or disappears. A few preliminary numerical examples are included to illustrate the model.