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

Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Aneta Wróblewska, Andrzej Warzyński (2009)

Banach Center Publications

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...

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