Annali di Matematica Pura ed Applicata (1923 -)

, Volume 196, Issue 3, pp 1185–1202 | Cite as

Homogenization of an incompressible stationary flow of an electrorheological fluid

  • Miroslav Bulíček
  • Martin Kalousek
  • Petr Kaplický
Article

Abstract

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.

Keywords

Non-Newtonian incompressible fluids Two-scale convergence Homogenization Lipschitz approximation 

Mathematics Subject Classification

35Q35 36B27 76M50 

Notes

Acknowledgments

We thank the anonymous referee for relevant remarks that helped to improve our article.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Miroslav Bulíček
    • 1
  • Martin Kalousek
    • 2
  • Petr Kaplický
    • 2
  1. 1.Mathematical InstituteCharles UniversityPraha 8, KarlínCzech Republic
  2. 2.Department of Mathematical AnalysisCharles UniversityPraha 8, KarlínCzech Republic

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