Comptes Rendus
Partial Differential Equations/Mathematical Problems in Mechanics
On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition
[Solutions continues en la viscosité pour les équations d'Euler ou de Navier–Stokes avec des conditions aux limites de type Navier]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1141-1146.

Pourvu que les données soient suffisamment régulières, il existe T0>0, ν>0 et {uν}0ν<ν famille unique de solutions fortes, locales en temps sur (0,T0) et dépendant continûment de ν, pour les problèmes d'Euler ou de Navier–Stokes. Ces solutions vérifient des conditions aux limites de type celles de Navier.

Provided the initial velocity and the external body force are sufficiently smooth, there exist T0>0, ν>0 and a unique continuous family of strong solutions uν (0ν<ν) of the Euler or Navier–Stokes initial–boundary value problem on the time interval (0,T0). The solutions of the Navier–Stokes problem satisfy a Navier-type boundary condition.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.09.007

Hamid Bellout 1 ; Jiří Neustupa 2 ; Patrick Penel 3

1 Northern Illinois University, Department of Mathematical Sciences, De Kalb, IL 60115, USA
2 Czech Technical University, Faculty of Mechanical Engineering, Department of Technical Mathematics, Karlovo nám. 13, 121 35 Praha 2, Czech Republic
3 Université du Sud Toulon-Var, département de mathématique et laboratoire SNC, BP 20132, 83957 La Garde cedex, France
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     title = {On viscosity-continuous solutions of the {Euler} and {Navier{\textendash}Stokes} equations with a {Navier-type} boundary condition},
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Hamid Bellout; Jiří Neustupa; Patrick Penel. On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1141-1146. doi : 10.1016/j.crma.2009.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.007/

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