Abstrakt
This article is concerned with the global regularity of weak solutions to systems describing the flow of shear thickening fluids under the homogeneous Dirichlet boundary condition. The extra stress tensor is given by a power law ansatz with shear exponent p larger or equal to 2.
We show that, if the data of the problem are smooth enough, the solution u of the steady generalized Stokes problem belongs to W1,q for suitable q. We use the method of tangential translations and reconstruct the regularity in the normal direction from the system, together with anisotropic embedding theorem.
Corresponding results for the steady and unsteady generalized Navier-Stokes problem are also formulated.