ON THE ROLE OF THE STOKES PROBLEM IN SECOND GRADE FLUID FLOW IN REGIONS WITH PERMEABLE INTERFACES

Abstract

The role of the Stokes problem in conducting a theory of existence of solutions, weak as well as classical, is under investigation in this research paper.  We model the motion of incompressible flows of non-Newtonian fluids through permeable boundaries in terms of the Stokes equation.  The equation of motion in the region Ω ∈ \(\mathbb{R}\)³ is coupled with the dynamic boundary condition through the permeable boundary Γ, in order to design a transport equation in a product space Y_m.  The existence of a unique solution for the Stokes problem is proved by using a special Helmholtz projection and employing the results from a paper of Agmon et al [1, Theorem 10.5 p.78].  The modelling is done for a special case where a ”shear flow” is assumed.