Electron. J. Diff. Equ., Vol. 2013 (2013), No. 196, pp. 1-28.

Stokes problem with several types of boundary conditions in an exterior domain

Cherif Amrouche, Mohamed Meslameni

Abstract:
In this article, we solve the Stokes problem in an exterior domain of $\mathbb{R}^{3}$, with non-standard boundary conditions. Our approach uses weighted Sobolev spaces to prove the existence, uniqueness of weak and strong solutions. This work is based on the vector potentials studied in [7] for exterior domains, and in [1] for bounded domains. This problem is well known in the classical Sobolev spaces $ W ^{m,2}(\Omega)$ when $\Omega$ is bounded; see [3,4].

Submitted July 28, 2013. Published September 3, 2013.
Math Subject Classifications: 35J25, 35J50, 76M30.
Key Words: Stokes equations; exterior domain; weighted Sobolev spaces; vector potentials; inf-sup conditions.

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Chérif Amrouche
Laboratoire de Mathématiques et de leurs Applications
Pau - CNRS UMR 5142, Université de Pau et des Pays de l'Adour
IPRA, Avenue de l'Université - 64000 Pau - France
email: cherif.amrouche@univ-pau.fr
  Mohamed Meslameni
Laboratoire de Mathématiques et de leurs Applications
Pau - CNRS UMR 5142, Université de Pau et des Pays de l'Adour
IPRA, Avenue de l'Université - 64000 Pau - France
email: mohamed.meslameni@univ-pau.fr

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