On the strong convergence of the solution of a generalized non-Newtonian fluid with Coulomb law in a thin film

Abstract

The goal of this paper is to examine the strong convergence of the velocity of a non-Newtonian incompressible fluid whose viscosity follows the power law with Coulomb friction. We assume that the fluid coefficients of the thin layer vary with respect to the thin layer parameter $ \varepsilon $. We give in a first step the description of the problem and basic equations. Then, we present the functional framework. The following paragraph is reserved for the main convergence results. Finally, we give the detail of the proofs of these results.

Keywords

• mathematical operators
• partial differential equations
• coulomb law
• non-newtonian fluid
• weak generalized equation
• variational inequality