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Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions

Published online by Cambridge University Press:  03 June 2015

M. Dilmi ,
H. Benseridi  and
A. Saadallah
M. Dilmi*
Affiliation:
Department of Mathematics, Faculty of Maths and Infs, M’sila University, 28000, Algeria
H. Benseridi*
Affiliation:
Applied Mathematics Laboratory, Department of Mathematics, Setif I-University, 19000, Algeria
A. Saadallah*
Affiliation:
Applied Mathematics Laboratory, Department of Mathematics, Setif I-University, 19000, Algeria
*
Corresponding author. Email: [email protected]
Email: [email protected]
Email: [email protected]
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Abstract

In this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition; then we study the asymptotic analysis when one dimension of the fluid domain tend to zero. The strong convergence of the velocity is proved, a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.

Keywords

35R3576F1078M35Free boundary problemsBingham fluidasymptotic approachTresca lawReynolds equation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 797 - 810
Copyright
Copyright © Global-Science Press 2014

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