ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

doi:10.1007/s10473-020-0308-1

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 700-712.doi: 10.1007/s10473-020-0308-1

ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

Adelkader SAADALLAH, Hamid BENSERIDI, Mourad DILMI

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

收稿日期:2018-11-26 出版日期:2020-06-25 发布日期:2020-07-17
作者简介:Adelkader SAADALLAH,E-mail:saadmath2009@gmail.com;Hamid BENSERIDI,E-mail:m_benseridi@yahoo.fr;Mourad DILMI,E-mail:mouraddil@yahoo.fr
基金资助:
The first author is supported by MESRS of Algeria (CNEPRU Project No. C00L03UN190120150002).

ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

Adelkader SAADALLAH, Hamid BENSERIDI, Mourad DILMI

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

Received:2018-11-26 Online:2020-06-25 Published:2020-07-17
Supported by:
The first author is supported by MESRS of Algeria (CNEPRU Project No. C00L03UN190120150002).

摘要/Abstract

摘要： 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.

关键词: Asymptotic approach, Herschel-Bulkley fluid, Reynolds equation, Tresca law

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.

Key words: Asymptotic approach, Herschel-Bulkley fluid, Reynolds equation, Tresca law

中图分类号:

35R35

Adelkader SAADALLAH, Hamid BENSERIDI, Mourad DILMI. ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2020, 40(3): 700-712.

Adelkader SAADALLAH, Hamid BENSERIDI, Mourad DILMI. ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS[J]. Acta mathematica scientia,Series B, 2020, 40(3): 700-712.

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ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

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