Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
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 li...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41510 |
| Acceso en línea: | http://hdl.handle.net/11441/41510 https://doi.org/10.1137/120873479 |
| Access Level: | acceso abierto |
| Palabra clave: | Navier–Stokes equations Navier condition rough boundary thin fluid films |
| Sumario: | 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. |
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