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...

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Detalles Bibliográficos
Autores: Casado Díaz, Juan, Luna Laynez, Manuel, Suárez Grau, Francisco Javier
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
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spelling Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundaryCasado Díaz, JuanLuna Laynez, ManuelSuárez Grau, Francisco JavierNavier–Stokes equationsNavier conditionrough boundarythin fluid filmsWe 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.Ministerio de Economía y Competitividad (España) MTM2011- 24457Junta de Andalucía FQM309Society for Industrial and Applied MathematicsEcuaciones Diferenciales y Análisis NuméricoMinisterio de Economía y Competitividad (MINECO). EspañaJunta de Andalucía2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41510https://doi.org/10.1137/120873479reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSIAM journal on mathematical analysis, 45 (3), 1641-1674.info:eu-repo/grantAgreement/MINECO/MTM2011- 24457/FQM309info:eu-repo/semantics/openAccessoai:idus.us.es:11441/415102026-06-17T12:51:07Z
dc.title.none.fl_str_mv Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
title Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
spellingShingle Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
Casado Díaz, Juan
Navier–Stokes equations
Navier condition
rough boundary
thin fluid films
title_short Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
title_full Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
title_fullStr Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
title_full_unstemmed Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
title_sort Asymptotic behavior of the Navier-Stokes system in a thin domain with Navier condition on a slightly rough boundary
dc.creator.none.fl_str_mv Casado Díaz, Juan
Luna Laynez, Manuel
Suárez Grau, Francisco Javier
author Casado Díaz, Juan
author_facet Casado Díaz, Juan
Luna Laynez, Manuel
Suárez Grau, Francisco Javier
author_role author
author2 Luna Laynez, Manuel
Suárez Grau, Francisco Javier
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Ministerio de Economía y Competitividad (MINECO). España
Junta de Andalucía
dc.subject.none.fl_str_mv Navier–Stokes equations
Navier condition
rough boundary
thin fluid films
topic Navier–Stokes equations
Navier condition
rough boundary
thin fluid films
description 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.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/41510
https://doi.org/10.1137/120873479
url http://hdl.handle.net/11441/41510
https://doi.org/10.1137/120873479
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv SIAM journal on mathematical analysis, 45 (3), 1641-1674.
info:eu-repo/grantAgreement/MINECO/MTM2011- 24457/
FQM309
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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