Unsteady flows of  non-Newtonian  fluids in generalized Orlicz spaces

Aneta Wróblewska-Kamińska

doi:10.3934/dcds.2013.33.2565

Article Contents

2013, Volume 33, Issue 6: 2565-2592. Doi: 10.3934/dcds.2013.33.2565

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Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces

Aneta Wróblewska-Kamińska^1,

1.
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa

Received: November 30, 2011

Revised: September 30, 2012

Published: June 2013

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Abstract

Our purpose is to show existence of weak solutions to unsteady flow of non-Newtonian incompressible nonhomogeneous fluids with nonstandard growth conditions of the stress tensor. We are motivated by the fluids of anisotropic behaviour and characterised by rapid shear thickening. Since we are interested in flows with the rheology more general than power-law-type, we describe the growth conditions with the help of an $x$--dependent convex function and formulate our problem in generalized Orlicz spaces.

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Mathematics Subject Classification: 35Q35, 46E30, 76D03.

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