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

摘要

The system -divS(D(u)) + (u-del)u+del 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.