[Remarque sur le problème du comportement asymptotique de l'écoulement d'un fluide incompressible autour d'un corps rigide en rotation]
Nous considérons des solutions faibles du système de Navier–Stokes stationnaire avec un terme d'Oseen et des termes rotationnels dans un domaine extérieur. Notre intérêt se porte sur la partie principale d'un développement asymptotique de la vitesse et de son gradient. Nous montrons que la vitesse peut être scindée, à des constantes près, en la première colonne de la solution fondamentale du système d'Oseen ( « tenseur d'Oseen »), plus un reste qui décroît ponctuellement dans un voisinage d'infini, à un taux qui est plus élevé que le taux de décroissance du tenseur d'Oseen. Ce résultat améliore la théorie présentée par M. Kyed [Asymptotic profile of a linearized flow past a rotating body, Q. Appl. Math. 71 (2013) 489–500 ; On the asymptotic structure of a Navier–Stokes flow past a rotating body, J. Math. Soc. Jpn. 66 (2014) 1–16].
We consider weak solutions to the stationary Navier–Stokes system with Oseen and rotational terms, in an exterior domain. We are interested in the leading term for the velocity field and its gradient. Moreover, we deal with the asymptotic behavior at infinity. We proved that the velocity may be split, within constants, into the first column of the fundamental solution to the Oseen system, plus a remainder term decaying pointwise near infinity at a rate which is higher than the decay rate of the Oseen tensor. This result improves the theory proposed by M. Kyed [Asymptotic profile of a linearized flow past a rotating body, Q. Appl. Math. 71 (2013) 489–500; On the asymptotic structure of a Navier–Stokes flow past a rotating body, J. Math. Soc. Jpn. 66 (2014) 1–16].
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@article{CRMATH_2016__354_8_794_0,
author = {Deuring, Paul and Kra\v{c}mar, Stanislav and Ne\v{c}asov\'a, \v{S}\'arka},
title = {Note to the problem of the asymptotic behavior of a viscous incompressible flow around a rotating body},
journal = {Comptes Rendus. Math\'ematique},
pages = {794--798},
publisher = {Elsevier},
volume = {354},
number = {8},
year = {2016},
doi = {10.1016/j.crma.2016.05.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.05.013/}
}
TY - JOUR AU - Deuring, Paul AU - Kračmar, Stanislav AU - Nečasová, Šárka TI - Note to the problem of the asymptotic behavior of a viscous incompressible flow around a rotating body JO - Comptes Rendus. Mathématique PY - 2016 SP - 794 EP - 798 VL - 354 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.05.013/ DO - 10.1016/j.crma.2016.05.013 LA - en ID - CRMATH_2016__354_8_794_0 ER -
%0 Journal Article %A Deuring, Paul %A Kračmar, Stanislav %A Nečasová, Šárka %T Note to the problem of the asymptotic behavior of a viscous incompressible flow around a rotating body %J Comptes Rendus. Mathématique %D 2016 %P 794-798 %V 354 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.05.013/ %R 10.1016/j.crma.2016.05.013 %G en %F CRMATH_2016__354_8_794_0
Deuring, Paul; Kračmar, Stanislav; Nečasová, Šárka. Note to the problem of the asymptotic behavior of a viscous incompressible flow around a rotating body. Comptes Rendus. Mathématique, Tome 354 (2016) no. 8, pp. 794-798. doi : 10.1016/j.crma.2016.05.013. http://www.numdam.org/articles/10.1016/j.crma.2016.05.013/
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