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. 261-272ISBN 978-80-87012-55-0 (Print)ISSN 2336-5781 (Print) |