Comptes Rendus
Partial differential equations
Solenoidal extensions of vector fields in two-dimensional unbounded domains
Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 481-485.

The goal of this note is to construct solenoidal extensions of vector fields defined on the boundary of simply connected domains having outlets to infinity and which satisfy the Leray–Hopf condition. The case of non-simply connected domains is also mentioned, in particular in the case when the domain admits a symmetry axis. This kind of extensions allows us to solve the stationary Navier–Stokes problem with nonhomogeneous boundary conditions in such domains.

Le but de cette note est la construction d'extensions de champs de vecteur definis sur la frontière de domaines simplement connexes ayant des canalisations allant à l'infini par des champs de vecteurs à divergence nulle satisfaisant la condition de Leray–Hopf. Le cas des ouverts non simplement connexes est évoqué, en particulier lorsque le domaine possède un axe de symétrie. Ces extensions permettent de résoudre les équations de Navier–Stokes avec des données au bord non homogènes dans ce type d'ouverts.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.02.010
Michel Chipot 1

1 Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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Michel Chipot. Solenoidal extensions of vector fields in two-dimensional unbounded domains. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 481-485. doi : 10.1016/j.crma.2016.02.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.02.010/

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