The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-law-type rheology. We describe the growth conditions with the help of general x-dependent convex functions. This formulation yields the existence of solutions in generalized Orlicz spaces. These considerations are motivated by e.g. electrorheological fluids, magnetorheological fluids, and shear thickening fluids.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-7,
author = {Piotr Gwiazda and Agnieszka \'Swierczewska-Gwiazda and Aneta Wr\'oblewska and Andrzej Warzy\'nski},
title = {Well-posedness for a class of non-Newtonian fluids with general growth conditions},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {115-128},
zbl = {1178.35131},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-7}
}
Piotr Gwiazda; Agnieszka Świerczewska-Gwiazda; Aneta Wróblewska; Andrzej Warzyński. Well-posedness for a class of non-Newtonian fluids with general growth conditions. Banach Center Publications, Tome 86 (2009) pp. 115-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-7/