Topical Problems of Fluid Mechanics


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Institute of Thermomechanics AS CR, v.v.i. CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics MIO Université du Sud Toulon Var - AMU - CNRS - IRD Czech Pilot centre ERCOFTAC
Non-Newtonian Fluids with Nonstandard Rheology - Existence of Solutions

Wróblewska-Kamińska A.

Abstract:
Our aim is to present a few results concerning existence of weak solutions to unsteady flow of incompressible non-Newtonian fluids. In particular, we are interested in dynamics of non- Newtonian fluids of a nonstandard rheology, more general then of power-law type. In considered problems the nonlinear highest order term - stress tensor - is monotone and its behaviour - coercivity/growth condition - is given with help of some general convex function. In our research we cover both cases: shear thickening and shear thinning uids and as well as anisotropic and non-homogenous behaviour of the stress tensor. Such a formulation requires a general framework for the function space setting, therefore we work with non-reexive and non-separable anisotropic Orlicz and Musielak-Orlicz spaces.

Keywords:
incompressible non-Newtonian fuids, weak solutions, Orlicz spaces, Musielak-Orlicz spaces
Fulltext: PDF
DOI: No Doi
In Proceedings Topical Problems of Fluid Mechanics 2015, Prague, 2015 Edited by David Šimurda and Tomáš Bodnár, pp. 261-272
ISBN 978-80-87012-55-0 (Print)
ISSN 2336-5781 (Print)
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