On a variational inequality for incompressible non-Newtonian thick flows

Abstract

In this work we extend the results on the existence, uniqueness and continuous dependence of strong solutions to a class of variational inequalities for incompressible non-Newtonian flows under the constraint of a variable maximum admissible shear rate. These fluids correspond to a limit case of shear-thickening viscosity, also called thick fluids, in which the solutions belong to a time dependent convex set with bounded deformation rate tensors. We also prove the existence of stationary solutions, which are the unique asymptotic limit of evolutionary flows in the case of sufficiently large viscosity.