Steady flow of fluids with smear-dependent viscosity under mixed boundary value conditions in polyhedral domains

In this paper the system of partial differential equations -div T(e) + (u . del)u + del pi = f, -div u = 0, is studied, where e is the symmetrized gradient of u, and T has p-structure for some p < 2 (e.g. div T is the p-Laplacian and p < 2). Mixed boundary v alue conditions on a three-dimensional polyhedral domain are considered. W- s,W-p-regularity (s = 3/2 - epsilon) of the velocity u and W-r,W-p'-regular ity of the pressure rr are proven.