On steady non-Newtonian fluids with growth conditions in generalized Orlicz spaces

Abstract

We are interested in the existence of weak solutions to steady non-Newtonian fluids with nonstandard growth conditions of the Cauchy stress tensor. Since the $L^p$ framework is not suitable to capture the description of strongly inhomogeneous fluids, we formulate the problem in generalized Orlicz spaces. The existence proof consists in showing that for Galerkin approximations the sequence of symmetric gradients of the flow velocity converges modularly. As an example of motivation for considering non-Newtonian fluids in generalized Orlicz spaces we recall the smart fluids.