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

• Autorzy: Piotr Gwiazda , Agnieszka Świerczewska-Gwiazda , Aneta Wróblewska , Andrzej Warzyński
• 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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 35Q35: PDEs in connection with fluid mechanics
• 35K55: Nonlinear parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 86
• Numer: 1
• Strony: 115-128

Daty

wydano

2009

Twórcy

autor

Piotr Gwiazda

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Agnieszka Świerczewska-Gwiazda

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Aneta Wróblewska

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Andrzej Warzyński

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc86-0-7