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2009 | 86 | 1 | 115-128

Tytuł artykułu

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

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Języki publikacji

EN

Abstrakty

EN
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.

Twórcy

  • Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
  • Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
  • Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

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Identyfikator YADDA

bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-7