Bayada, G.; Chambat, M. Sur quelques modélisations de la zone de cavitation en lubrification hydrodynamique. (Some modelling of the cavitation region in hydrodynamic lubrication). (French) Zbl 0621.76030 J. Méc. Théor. Appl. 5, 703-729 (1986). After a survey of some classical models, we study a new approach to the free boundary problem of the cavitation in hydrodynamic lubrication. This leads to a partial differential equation with a discontinuous nonlinearity; a mathematical study is carried out for two usual shapes of bearings. A finite elements procedure allows us to compute the operational data for a lubricated system with the new model and to compare them with those computed with another model based upon variational inequalities. Cited in 25 Documents MSC: 76D08 Lubrication theory 49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX) 76M99 Basic methods in fluid mechanics Keywords:Sommerfeld model; Reynolds model; free boundary problem; cavitation; hydrodynamic lubrication; bearings; finite elements procedure; lubricated system; variational inequalities PDF BibTeX XML Cite \textit{G. Bayada} and \textit{M. Chambat}, J. Méc. Théor. Appl. 5, 703--729 (1986; Zbl 0621.76030)