2016-05-232016-05-232013Casado Díaz, J., Luna Laynez, M. y Suárez Grau, F.J. (2013). Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary. SIAM journal on mathematical analysis, 45 (3), 1641-1674.0036-14101095-7154http://hdl.handle.net/11441/41510We study the asymptotic behavior of the solutions of the Navier–Stokes system in a thin domain Ωε of thickness ε satisfying the Navier boundary condition on a periodic rough set Γε ⊂ ∂Ωε of period rε and amplitude δε, with δε rε ε. We prove that the limit behavior as ε goes to zero depends on the limit λ of δεε 1 2 /r 3 2 ε . Namely, if λ = +∞, the roughness is so strong that the fluid behaves as if we had imposed the adherence condition on Γε. If λ = 0, the roughness is too weak and the fluid behaves as if Γε were a plane. Finally, if λ ∈ (0, +∞), the roughness is strong enough to make a new friction term appear in the limit.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Navier–Stokes equationsNavier conditionrough boundarythin fluid filmsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1137/120873479