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Effective fluid behavior in domain with rough boundary and the Darcy-Weisbach law

We derive the effective equations describing the behavior of the fluid in strap with rugged boundary. Starting from the Navier-Stokes system in domain with periodically perturbed boundary, we compute the asymptotic expansion of the solution. Using the expansion we obtain a 2D version of the Darcy-Weisbach law.

Navier-Stokes equations, asymptotic analysis, boundary layer, rough boundary, Darcy-Weisbach law

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