Well-posedness for a class of non-Newtonian fluids with general growth conditions

Piotr Gwiazda, et al. "Well-posedness for a class of non-Newtonian fluids with general growth conditions." Banach Center Publications 86.1 (2009): 115-128. <http://eudml.org/doc/282218>.

@article{PiotrGwiazda2009,
abstract = {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.},
author = {Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Aneta Wróblewska, Andrzej Warzyński},
journal = {Banach Center Publications},
keywords = {measure-valued solutions, Orlicz spaces; electrorheological fluids; magnetorheological fluids; shear thickening fluids},
language = {eng},
number = {1},
pages = {115-128},
title = {Well-posedness for a class of non-Newtonian fluids with general growth conditions},
url = {http://eudml.org/doc/282218},
volume = {86},
year = {2009},
}

TY - JOUR
AU - Piotr Gwiazda
AU - Agnieszka Świerczewska-Gwiazda
AU - Aneta Wróblewska
AU - Andrzej Warzyński
TI - Well-posedness for a class of non-Newtonian fluids with general growth conditions
JO - Banach Center Publications
PY - 2009
VL - 86
IS - 1
SP - 115
EP - 128
AB - 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.
LA - eng
KW - measure-valued solutions, Orlicz spaces; electrorheological fluids; magnetorheological fluids; shear thickening fluids
UR - http://eudml.org/doc/282218
ER -