On the plane steady-state flow of a shear-thinning liquid past an obstacle in the singular case

We show existence of strong solutions to the steady-state, two-dimensional exterior problem for a class of shear-thinning liquids –where shear viscosity is a suitable decreasing function of shear rate– for data of arbitrary size. Notice that the analogous problem is, to date, open for liquids governed by the Navier-Stokes equations, where viscosity is constant. Two important features of this work are that, on the one hand and unlike previous contributions by the same authors, the current results do not require non-vanishing of the constant-viscosity part of the stress tensor, and, on the other hand, we allow the shear-thinning contribution to be “arbitrarily small”, and, therefore, the model used here can be as “close” as we please to the classical Navier-Stokes one.