Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 196, pp. 1-28.
Title: Stokes problem with several types of boundary conditions in an exterior domain
Authors: Cherif Amrouche (Univ. de Pau et des Pays de l'Adour, Pau, France)
Mohamed Meslameni (Univ. de Pau et des Pays de l'Adour, Pau, France)
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 03, 2013.
Math Subject Classifications: 35J25, 35J50, 76M30.
Key Words: Stokes equations; exterior domain; weighted Sobolev spaces;
vector potentials; inf-sup conditions.