Quasi-steady Stokes flow of multiphase fluids with shear-dependent viscosity

Abstract

The quasi–steady power–law Stokes flow of a mixture of incompressible fluids with shear–dependent viscosity is studied. The fluids are immiscible and have constant densities. Existence results are presented for both the no–slip and the no–stick boundary value conditions. Use is made of Schauder’s fixed–point theorem, compactness arguments, and DiPerna-Lions renormalized solutions.