Stationary Flows of Shear Thickening Fluids in 2D

We investigate the steady flow of a shear thickening generalized Newtonian fluid under homogeneous boundary conditions on a domain in R-2. We assume that the stress tensor is generated by a potential of the form H = h(|epsilon( u)|), epsilon(u) denoting the symmetric part of the velocity gradient. We prove the existence of strong solutions for a large class of functions h having the property that h'(t)/t increases (shear thickening case).