Existence Results for Steady Flows of Quasi-Newtonian Fluids Using Weak Monotonicity

This work is concerned with the study of steady flows of an incompressible quasi-Newtonian fluid, with viscosity depending on the second invariant of the rate of deformation tensor, in bounded domains. We first establish a result of existence of measure-valued solutions. Next, we prove that under some natural monotonicity conditions, these solutions are weak.