Existence of solution of an elastohydrodynamic Reynolds–Koiter model

Abstract

In this paper the existence of solution for a new elastohydrodynamic model for journal bearing devices is proved. The lubricant pressure and the concentration are governed by Reynolds equation combined with Elrod–Adams model for cavitation, while the bearing displacement follows a Koiter model for shells. A regularization procedure is proposed to overcome the Heaviside concentration–pressure relation. A fixed point theorem leads to the solution of the regularized problem. The introduction of prolongation and restriction operators copes with the additional difficulty of elastic and hydrodynamic subproblems posed on different domains. The estimates for the regularized problem allow to pass to the limit and state the existence result.