Abstrakt
Navier-Stokes equations represents a key reference model both in the analysis of nonlinear partial differential systems, and in non-Newtonian fluid mechanics. The power-law fluid, one of the most popular non-Newtonian models, generalizes the Navier-Stokes fluid in the fact that its non-constant viscosity is a power of the shear rate.
A modification of the power-law fluids that consists in multi plying the power of the shear rate by the pressure is also considered. Such a model fits to the class of fluids with the viscosity depending on the shear rate and on the the pressure.
We look at all these models from the point of view of invariance with respect to suitable scaling, and present some relevant results and open problems.