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In this paper we derive consistent shallow water equations for thin films ofpower law fluids down an incline. These models account for the streamwisediffusion of momentum which is important to describe accurately the fulldynamic of the thin film flows when instabilities like roll-waves arise. Thesemodels are validated through a comparison with Orr Sommerfeld equations forlarge scale perturbations. We only consider laminar flow for which the boundarylayer issued from the interaction of the flow with the bottom surface has aninfluence all over the transverse direction to the flow. In this case theconcept itself of thin film and its relation with long wave asymptotic leadsnaturally to flow conditions around a uniform free surface Poiseuille flow. Theapparent viscosity diverges at the free surface which, in turn, introduces asingularity in the formulation of the Orr-Sommerfeld equations and in thederivation of shallow water models. We remove this singularity by introducing aweaker formulation of Cauchy momentum equations. No regularization procedure isneeded nor distinction between shear thinning/thickening cases. Our analysis isonly valid when the flow behavior index $n$ is larger than 1/2 and stronglysuggests that the equations are ill posed if $n<1/2$.

Thin power law film flow down an inclined plane: consistent shallow water models and stability under large scale perturbations