Effect of rugosity on a flow governed by stationary Navier-Stokes equations

Amirat, Youcef; Bresch, Didier; Lemoine, Jérôme; Simon, Jacques

doi:10.1090/qam/1866556

Authors: Youcef Amirat, Didier Bresch, Jérôme Lemoine and Jacques Simon
Journal: Quart. Appl. Math. 59 (2001), 769-785
MSC: Primary 76D05; Secondary 76M45
DOI: https://doi.org/10.1090/qam/1866556
MathSciNet review: MR1866556
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Abstract: We study the stationary flow of a fluid occupying a 3D infinite horizontal domain bounded by a rough wall that is at rest and by a plane that moves with a constant velocity. The rough wall is a plane covered with periodically distributed asperities of size $\varepsilon$. We prove that, outside a neighbourhood of the rough region, the flow behaves asymptotically as a Couette flow, as $\varepsilon \to 0$, up to an exponentially small error.

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