[Régularité conditionnelle jusqu'à la frontière du domaine en théorie des équations de Navier–Stokes associées à des conditions limites d'imperméabilité généralisée]
Dans cette Note, nous étendons jusqu'à la frontière du domaine spatial, les conditions suffisantes pour la régularité des solutions faibles des équations de Navier–Stokes que nous avions obtenues dans nos travaux précédents. Ces conditions sont basées sur les propriétés d'intégrabilité ou bien d'une des valeurs propres du tenseur de déformation, ou bien d'une des composantes du champ de vitesse.
In this Note, we extend sufficient conditions for regularity we described in our previous works so that they are valid not only in the interior, but up to the boundary of a flow field. The conditions are based on the integrability properties of either one of the eigenvalues of the rate of deformation tensor or one component of velocity.
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@article{CRMATH_2005__340_1_31_0,
author = {Neustupa, Ji\v{r}{\'\i} and Penel, Patrick},
title = {On the regularity up to the boundary in the theory of the {Navier{\textendash}Stokes} equations with generalized impermeability conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {31--36},
publisher = {Elsevier},
volume = {340},
number = {1},
year = {2005},
doi = {10.1016/j.crma.2004.10.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.10.016/}
}
TY - JOUR AU - Neustupa, Jiří AU - Penel, Patrick TI - On the regularity up to the boundary in the theory of the Navier–Stokes equations with generalized impermeability conditions JO - Comptes Rendus. Mathématique PY - 2005 SP - 31 EP - 36 VL - 340 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.10.016/ DO - 10.1016/j.crma.2004.10.016 LA - en ID - CRMATH_2005__340_1_31_0 ER -
%0 Journal Article %A Neustupa, Jiří %A Penel, Patrick %T On the regularity up to the boundary in the theory of the Navier–Stokes equations with generalized impermeability conditions %J Comptes Rendus. Mathématique %D 2005 %P 31-36 %V 340 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.10.016/ %R 10.1016/j.crma.2004.10.016 %G en %F CRMATH_2005__340_1_31_0
Neustupa, Jiří; Penel, Patrick. On the regularity up to the boundary in the theory of the Navier–Stokes equations with generalized impermeability conditions. Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 31-36. doi : 10.1016/j.crma.2004.10.016. http://www.numdam.org/articles/10.1016/j.crma.2004.10.016/
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[8] J. Neustupa, P. Penel, Two results on regularity up to the boundary of a weak solution to the Navier–Stokes equation in a bounded smooth domain, in preparation
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