Amirat, Youcef; Bresch, Didier; Lemoine, Jérôme; Simon, Jacques Effect of rugosity on a flow governed by stationary Navier-Stokes equations. (English) Zbl 1019.76014 Q. Appl. Math. 59, No. 4, 769-785 (2001). 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. Cited in 33 Documents 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 Keywords:rugosity; stationary Navier-Stokes equations; Couette flow; exponentially small error PDFBibTeX XMLCite \textit{Y. Amirat} et al., Q. Appl. Math. 59, No. 4, 769--785 (2001; Zbl 1019.76014) Full Text: DOI