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

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Gwiazda P., Świerczewska-Gwiazda A., Wróblewska A., Warzyński A.

Banach Center Publications

2009

tom 86

nr 1

115-128

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.

Ograniczanie wyników

1 Banach Center Publications

1 Gwiazda P.

1 Warzyński A.

1 Wróblewska A.

1 Świerczewska-Gwiazda A.

1 2009

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