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 mathbbR²{mathbb{R}^{2}}. We assume that the stress tensor is generated by a potential of the form H = h (|e(u)|){H = h (|varepsilon (u)|)}, e(u){varepsilon (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).