On a non-stationary, non-Newtonian lubrication problem with Tresca fluid-solid law

Abstract

AbstractThe paper deals with the theoretical analysis of a non-Newtonian lubrication problem in a dynamic regime in a three-dimensional thin domain{\Omega^{\varepsilon}}with Tresca friction law. The problem statement and variational formulation of the problem are formulated. Then the problem is reformulated in a fixed domain, in which case the estimates on velocity and pressure are proved. These estimates are useful in order to give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.