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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.

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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