Asymptotic Convergence of a Generalized Non-Newtonian Fluid with Tresca Boundary Conditions

Abstract

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameter e. Firstly, the problem statement and variational formulation are formulated. We then obtained the existence and the uniqueness result of a weak solution and the estimates for the velocity field and the pressure independently of the parameter e. Finally, we give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.