Steady flow for shear thickening fluids in domains with unbounded sections

We solve the stationary Stokes and Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with outlets containing unbounded cross sections, in the case of shear thickening viscosity. The flux assumes arbitrary given values and the growth of the cross sections are analyzed under different convergence hypotheses, inclusive the growth of Dirichlet's integral of the velocity field is deeply related the convergence hypotheses of such sections. We extend the results of the section 4 of [12, Ladyzhenskaya and Solonnikov] (for Newtonian fluids) to non-Newtonian fluids using the techniques found in [3, Dias and Santos].