Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Asymptotic behaviour of solutions of lubrication problem in a thin domain with a rough boundary and Tresca fluid-solid interface law

Authors: Mahdi Boukrouche and Ionel Ciuperca
Journal: Quart. Appl. Math. 64 (2006), 561-591
MSC (2000): Primary 35R35, 35J85, 78M35, 78M40, 74K35
DOI: https://doi.org/10.1090/S0033-569X-06-01030-3
Published electronically: July 18, 2006
MathSciNet review: 2259055
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Abstract: We study the asymptotic behavior of the solution of a Stokes flow in a thin domain, with a thickness of order $ \varepsilon$, and a rough surface. The roughness is defined by a quasi-periodic function with period $ \varepsilon$. We suppose that the flow is subject to a Tresca fluid-solid interface condition. We prove a new result on the lower-semicontinuity for the two-scale convergence, which allows us to obtain rigorously the limit problem and to establish the uniqueness of its solution.

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Mahdi Boukrouche
Affiliation: Laboratory of Mathematics, University of Saint-Etienne, EA 3989, 23 rue Dr. Paul Michelon, 42023 Saint-Etienne, France
Email: Mahdi.Boukrouche@univ-st-etienne.fr

Ionel Ciuperca
Affiliation: Institut Camille Jordan, Université Lyon 1, UMR 5208, France
Email: ciuperca@math.univ-lyon1.fr

DOI: https://doi.org/10.1090/S0033-569X-06-01030-3
Keywords: Free boundary problem, Lubrication, Rough boundary, Tresca fluid-solid conditions, Homogenization, Lower-semicontinuity for the two-scale convergence, Reynolds equation.
Received by editor(s): January 27, 2006
Published electronically: July 18, 2006
Article copyright: © Copyright 2006 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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