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Free boundary problems in the theory of hydrodynamic lubrication: A survey. (English) Zbl 0557.76038
Free boundary problems, theory and applications, Vol. II, Proc. interdisc. Symp., Montecatini/Italy 1981, Res. Notes Math. 79, 613-635 (1983).
[For the entire collection see Zbl 0504.00012.]
The paper is a comprehensive study of the free boundary problem in the theory of lubrication, presentable as an appropriate variational inequality. The first three sections contain a compact review of the main results from the earlier work of the authors [e.g.: the second author, Int. J. Eng. Sci. 18, 703-711 (1980; Zbl 0456.76009)] and also some new results. In particular a complete description of the geometrical properties of the region of cavitation for the case of journal bearing of small eccentricity ratio is given. In the next sections, the classical solutions of Sommerfeld and Ocvirk are justified from a rigorous mathematical point of view. The authors conclude the paper by discussing the controversial problem of the conditions which must be imposed on the boundary of the region of cavitation.
Reviewer: J.Prakash

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D05 Navier-Stokes equations for incompressible viscous fluids
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics