TY - JOUR AU - Gwiazda, Piotr AU - ƚwierczewska-Gwiazda, Agnieszka PY - 2008/09/01 Y2 - 2024/03/29 TI - On steady non-Newtonian fluids with growth conditions in generalized Orlicz spaces JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 32 IS - 1 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2008.038 SP - 103 - 113 AB - We are interested in the existence of weak solutions to steady non-Newtonianfluids with nonstandard growth conditions of the Cauchy stress tensor.Since the $L^p$ framework is not suitable to capture the descriptionof 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 velocityconverges modularly.As an example of motivation forconsidering non-Newtonian fluids in generalized Orlicz spaces werecall the smart fluids. ER -