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

Tom 86 / 2009

Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Aneta Wróblewska, Andrzej Warzyński Banach Center Publications 86 (2009), 115-128 MSC: 35K55, 35Q35, 46E30. DOI: 10.4064/bc86-0-7

Streszczenie

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.

Autorzy

  • Piotr GwiazdaInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Agnieszka Świerczewska-GwiazdaInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Aneta WróblewskaInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Andrzej WarzyńskiFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warszawa, Poland
    e-mail

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