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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 1, 1995, pp. 59–87
DOI: 10.4171/ZAA/663

Published online: 1995-03-31

The Transient Lubrication Problem as a Generalized Hele-Shaw Type Problem

G. Bayada[1], M. Boukrouche[2] and M. El-A. Talibi[3]

(1) Université Lyon 1, Villeurbanne, France
(2) Université Lyon 1, Villeurbanne, France
(3) Université Cadi Ayyad, Marrakech, Morocco

The aim of this paper is to bridge the gap between Hele-Shaw theory and lubrication theory. A first generalization of the Hele-Shaw problem is considered for which existence, uniqueness and regularity theorems are given. Then taking shear effects into account, lubrication fluid mixture approach has to be used, inducing a new formulation of the initial problem. Connection of the two kind of problems are then given, establishing Ilele-Shaw phenomena as a particular case of lubrication problem on a mathematical basis.

Keywords: Hele-Shaw flow, cavitation phenomena, free boundary Reynolds equations, Darcy’s law, variational inequalities

Bayada G., Boukrouche M., Talibi M. El-A.: The Transient Lubrication Problem as a Generalized Hele-Shaw Type Problem. Z. Anal. Anwend. 14 (1995), 59-87. doi: 10.4171/ZAA/663