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

Boukrouche, Mahdi; Ciuperca, Ionel

doi:10.1090/S0033-569X-06-01030-3

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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