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Asymptotic Convergence of a Generalized Non-Newtonian Fluid with Tresca Boundary Conditions

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Abstract

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameter ε. Firstly, the problem statement and variational formulation are formulated. We then obtained the existence and the uniqueness result of a weak solution and the estimates for the velocity field and the pressure independently of the parameter ε. Finally, we give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

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Acknowledgements

The authors thank Prof. El-Bachir Yallaoui for his help in revising the English language in the article.

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Authors and Affiliations

  1. Applied Mathematics Laboratory, Department of Mathematics, Faculty of Sciences, University of Ferhat Abbas, Sétif 1, 19000, Algeria

    Adelkader Saadallah, Hamid Benseridi & Mourad Dilmi

Authors
  1. Adelkader Saadallah
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  2. Hamid Benseridi
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  3. Mourad Dilmi
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Corresponding authors

Correspondence to Adelkader Saadallah, Hamid Benseridi or Mourad Dilmi.

Additional information

The first author is supported by MESRS of Algeria (CNEPRU Project No. C00L03UN190120150002).

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Saadallah, A., Benseridi, H. & Dilmi, M. Asymptotic Convergence of a Generalized Non-Newtonian Fluid with Tresca Boundary Conditions. Acta Math Sci 40, 700–712 (2020). https://doi.org/10.1007/s10473-020-0308-1

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  • DOI: https://doi.org/10.1007/s10473-020-0308-1

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