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Effect of rugosity on a flow governed by stationary Navier-Stokes equations. (English) Zbl 1019.76014
Summary: We study the stationary flow of fluid occupying a three-dimensional 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 Couette flow, as \(\varepsilon\to 0\), up to an exponentially small error.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
35Q30 Navier-Stokes equations
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