Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    5 0 0 0


Comptes Rendus Mathématique
Volume 357, n° 2
pages 115-119 (février 2019)
Doi : 10.1016/j.crma.2018.12.002
Received : 18 June 2018 ;  accepted : 7 December 2018
Stokes and Navier–Stokes equations with Navier boundary condition
Équations de Stokes et de Navier–Stokes avec la condition de Navier
 

Paul Acevedo a , Chérif Amrouche b , Carlos Conca c , Amrita Ghosh b, d
a Escuela Politécnica Nacional, Departamento de Matemática, Facultad de Ciencias, Ladrón de Guevara E11-253, P.O. Box 17-01-2759, Quito, Ecuador 
b LMAP, UMR CNRS 5142, Bâtiment IPRA, avenue de l'Université, BP 1155, 64013 Pau cedex, France 
c Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile 
d Departamento de Matemáticas, Facultad de Ciencias y Tecnología, Universidad del País Vasco, Barrio Sarriena s/n, 48940 Lejona, Vizcaya, Spain 

Abstract

In this paper, we study the stationary Stokes and Navier–Stokes equations with non-homogeneous Navier boundary condition in a bounded domain   of class   from the viewpoint of the behavior of solutions with respect to the friction coefficient α . We first prove the existence of a unique weak solution (and strong) in   (and  ) to the linear problem for all   considering minimal regularity of α , using some inf–sup condition concerning the rotational operator. Furthermore, we deduce uniform estimates of the solutions for large α , which enables us to obtain the strong convergence of Stokes solutions with Navier slip boundary condition to the one with no-slip boundary condition as  . Finally, we discuss the same questions for the non-linear system.

The full text of this article is available in PDF format.
Résumé

Dans cette note, nous étudions les équations stationnaires de Stokes et de Navier–Stokes avec une condition aux limites non homogène de Navier dans un domaine borné   de classe  , et envisageons le comportement des solutions par rapport au coefficient de friction α . Nous prouvons, d'abord dans le cas linéaire, l'existence d'une solution faible (et d'une solution forte) unique dans   (et  ) pour tout   en supposant α le moins régulier possible et en utilisant une condition inf–sup concernant l'opérateur rotationnel. De plus, nous déduisons des estimations uniformes des solutions pour α grand, qui nous permettent d'obtenir la convergence forte des solutions de Stokes avec la condition de glissement vers les solutions vérifiant la condition d'adhérence lorsque  . Finalement, nous étudions les mêmes questions pour le système non linéaire.

The full text of this article is available in PDF format.


© 2018  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline