×

Convergence of the rotating fluids system in a domain with rough boundaries. (English) Zbl 1229.76106

Journées “Équations aux dérivées partielles”, Forges-les-Eaux, France, 2 au 6 juin 2003. Exposés Nos. I-XV. Nantes: Université de Nantes (ISBN 2-86939-207-9/pbk). Exp. No. VIII, 15 p. (2003).
Summary: We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size \(\varepsilon\). We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as \(\varepsilon\) goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical Ekman layers.
For the entire collection see [Zbl 1027.00017].

MSC:

76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
86A05 Hydrology, hydrography, oceanography