Mathematical analysis of some new Reynolds-rod elastohydrodynamic models

In this paper, some new elastohydrodynamic Reynolds-rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic r od displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displac ement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove t he existence of solution. Besides nearly linear coupled problems, two non-l inear rod problems including curvature effects are analysed. Mainly, regula rity results and L-infinity estimates for the solution of variational inequ alities and fixed-point theorems lead to the existence results for the vari ous coupled models. Copyright (C) 2001 John Wiley & Sons, Ltd.