[Extensions de champs de vecteurs dans des ouverts non bornés]
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.
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.
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@article{CRMATH_2016__354_5_481_0,
author = {Michel Chipot},
title = {Solenoidal extensions of vector fields in two-dimensional unbounded domains},
journal = {Comptes Rendus. Math\'ematique},
pages = {481--485},
publisher = {Elsevier},
volume = {354},
number = {5},
year = {2016},
doi = {10.1016/j.crma.2016.02.010},
language = {en},
}
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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