[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.
Accepté le :
Publié le :
Jiřı́ Neustupa 1 ; Patrick Penel 2
@article{CRMATH_2003__336_10_805_0,
author = {Ji\v{r}{\i}́ Neustupa and Patrick Penel},
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},
}
TY - JOUR AU - Jiřı́ Neustupa AU - Patrick Penel 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 DO - 10.1016/S1631-073X(03)00174-2 LA - en ID - CRMATH_2003__336_10_805_0 ER -
%0 Journal Article %A Jiřı́ Neustupa %A Patrick Penel %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 %R 10.1016/S1631-073X(03)00174-2 %G en %F CRMATH_2003__336_10_805_0
Jiřı́ Neustupa; Patrick Penel. The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier–Stokes equations. Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 805-810. doi : 10.1016/S1631-073X(03)00174-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00174-2/
[1] Partial regularity of suitable weak solutions of the Navier–Stokes equations, Comm. Pure Appl. Math., Volume 35 (1982), pp. 771-831
[2] An Introduction to the Navier–Stokes initial-boundary value problem (G.P. Galdi; J. Heywood; R. Rannacher, 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 (J. Neustupa; P. Penel, 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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