Steady flow of non-Newtonian fluids — monotonicity methods in generalized Orlicz spaces

Our purpose is to show the existence of weak solutions to steady flow of non-Newtonian incompressible fluids with nonstandard growth conditions of the Cauchy stress tensor. We are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening. Since LpLp framework is not sufficient to capture the described model, we describe the growth conditions with the help of a general xx-dependent convex function and formulate our problem in generalized Orlicz spaces.