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Highly rotating fluids in rough domains. (English) Zbl 1033.76008
Summary: We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed to be of characteristic size \(\varepsilon\). We prove a strong convergence theorem for solutions of Navier-Stokes-Coriolis equations, as \(\varepsilon\) goes to 0, in the well-prepared case. We show, in particular, that the limit system contains a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus give a substantial refinement of the results obtained on flat boundaries with classical Ekman layers.

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
35Q30 Navier-Stokes equations
Full Text: DOI
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