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Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary

 

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Opened Access Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
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Author: Casado Díaz, Juan
Luna Laynez, Manuel
Suárez Grau, Francisco Javier
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2013
Published in: SIAM journal on mathematical analysis, 45 (3), 1641-1674.
Document type: Article
Abstract: We 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.
Cite: Casado 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.
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URI: http://hdl.handle.net/11441/41510

DOI: http://dx.doi.org/10.1137/120873479

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