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

摘要

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