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

Abstract

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.