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Volume 6, Issue 6
Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions

M. Dilmi, H. Benseridi & A. Saadallah

DOI: 10.4208/aamm.2013.m350

Adv. Appl. Math. Mech., 6 (2014), pp. 797-810.

Published online: 2014-06

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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 tends to zero. The strong convergence of the velocity is proved, and a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.

  • Keywords

Free boundary problems, Bingham fluid, asymptotic approach, Tresca law, Reynolds equation.

  • AMS Subject Headings

35R35, 76F10, 78M35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-797, author = {Dilmi , M.Benseridi , H. and Saadallah , A.}, title = {Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {6}, pages = {797--810}, 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 tends to zero. The strong convergence of the velocity is proved, and a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m350}, url = {http://global-sci.org/intro/article_detail/aamm/49.html} }
TY - JOUR T1 - Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions AU - Dilmi , M. AU - Benseridi , H. AU - Saadallah , A. JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 797 EP - 810 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m350 UR - https://global-sci.org/intro/article_detail/aamm/49.html KW - Free boundary problems, Bingham fluid, asymptotic approach, Tresca law, Reynolds equation. AB -

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 tends to zero. The strong convergence of the velocity is proved, and a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.

Dilmi , M.Benseridi , H. and Saadallah , A.. (2014). Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions. Advances in Applied Mathematics and Mechanics. 6 (6). 797-810. doi:10.4208/aamm.2013.m350
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