Cherif Amrouche, Mohamed Meslameni
Abstract:
In this article, we solve the Stokes problem in an exterior domain of
,
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
when
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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