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

The system$${-{\rm{div}}\,{\rm\bf{S}}({\rm\bf{D}}({\rm\bf{u}}))+({\rm\bf{u}}\cdot\nabla){\rm\bf{u}}+\nabla\pi\,{=}\,{\rm\bf{f}}, \quad{\rm{div}}\,{\rm\bf{u}}\,{=}\,0}$$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 π in fractional order Sobolev and Nikolskii spaces are obtained. Copyright © 2006 John Wiley & Sons, Ltd.