Regularity in Sobolev spaces of steady flows of fluids with shear-dependent viscosity

The system -div S(D(u))+(u.(nabla))u+(nabla)(pi)=f, div u=0 is considered on a bounded three-dimensional domain under no-stick boundary value conditions, where S has p-structure for some p<2 and D(u) is the symmetrized gradient of u. Various regularity results for the velocity u and the pressure (pi)in fractional order Sobolev and Nikolskii spaces are obtained.