Homogenization of an incompressible stationary flow of an electrorheological fluid

We combine two-scale convergence, theory of monotone operators and results on approximation of Sobolev functions by Lipschitz functions to prove a homogenization process for an incompressible flow of a generalized Newtonian fluid. We avoid the necessity of testing the weak formulation of the initial...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2017-06, Vol.196 (3), p.1185-1202
Main Authors: Bulíček, Miroslav, Kalousek, Martin, Kaplický, Petr
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Electrorheological fluids
Fluid flow
Homogenization
Incompressible flow
Mathematics
Mathematics and Statistics
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Summary:We combine two-scale convergence, theory of monotone operators and results on approximation of Sobolev functions by Lipschitz functions to prove a homogenization process for an incompressible flow of a generalized Newtonian fluid. We avoid the necessity of testing the weak formulation of the initial and homogenized systems by corresponding weak solutions, which allows optimal assumptions on lower bound for a growth of the elliptic term. We show that the stress tensor for homogenized problem depends on the symmetric part of the velocity gradient involving the limit of a sequence selected from a family of solutions of initial problems.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-016-0612-5