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Comptes Rendus Mathématique
Volume 347, n° 19-20
pages 1141-1146 (octobre 2009)
Doi : 10.1016/j.crma.2009.09.007
Received : 6 June 2009 ;  accepted : 9 September 2009
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

Hamid Bellout a , Jiří Neustupa b , Patrick Penel c
a Northern Illinois University, Department of Mathematical Sciences, De Kalb, IL 60115, USA 
b Czech Technical University, Faculty of Mechanical Engineering, Department of Technical Mathematics, Karlovo nám. 13, 121 35 Praha 2, Czech Republic 
c Université du Sud Toulon-Var, département de mathématique et laboratoire SNC, BP 20132, 83957 La Garde cedex, France 


Provided the initial velocity and the external body force are sufficiently smooth, there exist  ,   and a unique continuous family of strong solutions   ( ) of the Euler or Navier–Stokes initial–boundary value problem on the time interval  . The solutions of the Navier–Stokes problem satisfy a Navier-type boundary condition. To cite this article: H. Bellout et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.

Pourvu que les données soient suffisamment régulières, il existe  ,   et   famille unique de solutions fortes, locales en temps sur   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. Pour citer cet article : H. Bellout et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.

© 2009  Published by Elsevier Masson SAS de la part de Académie des sciences.
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