Study of generalized Stokes operator in a thin domain with friction law (case p < 2)

Abstract

In this work, we consider a mathematical model of an incompressible fluid governed by the generalized Stokes system in a stationary regime in a 3‐dimensional thin domain Ωϵ with Tresca friction law. The problem statement and variational formulation of the problem are formulated. Then the estimates on velocity and pressure are proved in a fixed domain. Finally, our main goal concerns the specific Reynolds equation and the uniqueness of the solution are obtained.