[Rôle des valeurs propres et des vecteurs propres du gradient symétrisé des vitesses en théorie des équations de Navier–Stokes]
Dans cette Note, on formule des conditions géométriques suffisantes pour la régularité intérieure des solutions faibles ( « suitable weak ») des équations de Navier–Stokes dans un sous-domaine D du cylindre spatio–temporel QT : ces conditions suffisantes portent sur une des valeurs propres ou bien sur les composantes des vecteurs propres du gradient symétrisé.
In this Note, we formulate sufficient conditions for regularity of a so called suitable weak solution (v;p) in a sub-domain D of the time–space cylinder QT by means of requirements on one of the eigenvalues or on the eigenvectors of the symmetrized gradient of velocity.
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@article{CRMATH_2003__336_10_805_0,
author = {Neustupa, Ji\v{r}{\i}́ and Penel, Patrick},
title = {The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the {Navier{\textendash}Stokes} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {805--810},
publisher = {Elsevier},
volume = {336},
number = {10},
year = {2003},
doi = {10.1016/S1631-073X(03)00174-2},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00174-2/}
}
TY - JOUR AU - Neustupa, Jiřı́ AU - Penel, Patrick TI - The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier–Stokes equations JO - Comptes Rendus. Mathématique PY - 2003 SP - 805 EP - 810 VL - 336 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00174-2/ DO - 10.1016/S1631-073X(03)00174-2 LA - en ID - CRMATH_2003__336_10_805_0 ER -
%0 Journal Article %A Neustupa, Jiřı́ %A Penel, Patrick %T The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier–Stokes equations %J Comptes Rendus. Mathématique %D 2003 %P 805-810 %V 336 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00174-2/ %R 10.1016/S1631-073X(03)00174-2 %G en %F CRMATH_2003__336_10_805_0
Neustupa, Jiřı́; Penel, Patrick. The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier–Stokes equations. Comptes Rendus. Mathématique, Tome 336 (2003) no. 10, pp. 805-810. doi : 10.1016/S1631-073X(03)00174-2. http://www.numdam.org/articles/10.1016/S1631-073X(03)00174-2/
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[2] An Introduction to the Navier–Stokes initial-boundary value problem (Galdi, G.P.; Heywood, J.; Rannacher, R., eds.), Fundamental Directions in Mathematical Fluid Mechanics, Birkhäuser, Basel, 2000, pp. 1-98
[3] Anisotropic and geometric criteria for interior regularity of weak solutions to the 3D Navier–Stokes equations (Neustupa, J.; Penel, P., eds.), Mathematical Fluid Mechanics, Recent Results and Open Problems, Birkhäuser, Basel, 2001, pp. 237-268
[4] J. Neustupa, P. Penel, Regularity of weak solutions to the Navier–Stokes equations in dependence on eigenvalues and eigenvectors of the rate of deformation tensor, Preprint, 2002
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