[Note sur les solutions statistiques des équations de Navier–Stokes incompressibles en dimension trois d'espace : le cas dépendant du temps]
Dans cette Note nous considérons les solutions statistiques des équations de Navier-Stokes incompressibles en dimension trois d'espace. Elles constituent une formalisation mathématique de la notion de moyenne statistique dans la théorie de la turbulence et forment l'un des fondements de la théorie mathématique de la turbulence. Deux notions différentes de solutions statistiques ont été introduites ; nous les rappelons et donnons une formulation nouvelle de l'une d'elles. Nous établissons en outre un théorème d'existence de solutions pour cette nouvelle notion, et donnons un certain nombre de propriétés utiles des solutions statistiques.
Time-dependent statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble averages in turbulence theory and form the backbone for a mathematical foundation of the theory of turbulence. The two main notions of statistical solutions, previously introduced, are revisited and a new formulation of one of them is given. An existence proof for this new formulation is given, along with a number of useful properties.
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Publié le :
Ciprian Foias 1 ; Ricardo M.S. Rosa 2 ; Roger Temam 3, 4
@article{CRMATH_2010__348_3-4_235_0,
author = {Ciprian Foias and Ricardo M.S. Rosa and Roger Temam},
title = {A note on statistical solutions of the three-dimensional {Navier{\textendash}Stokes} equations: {The} time-dependent case},
journal = {Comptes Rendus. Math\'ematique},
pages = {235--240},
publisher = {Elsevier},
volume = {348},
number = {3-4},
year = {2010},
doi = {10.1016/j.crma.2009.12.017},
language = {en},
}
TY - JOUR AU - Ciprian Foias AU - Ricardo M.S. Rosa AU - Roger Temam TI - A note on statistical solutions of the three-dimensional Navier–Stokes equations: The time-dependent case JO - Comptes Rendus. Mathématique PY - 2010 SP - 235 EP - 240 VL - 348 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2009.12.017 LA - en ID - CRMATH_2010__348_3-4_235_0 ER -
%0 Journal Article %A Ciprian Foias %A Ricardo M.S. Rosa %A Roger Temam %T A note on statistical solutions of the three-dimensional Navier–Stokes equations: The time-dependent case %J Comptes Rendus. Mathématique %D 2010 %P 235-240 %V 348 %N 3-4 %I Elsevier %R 10.1016/j.crma.2009.12.017 %G en %F CRMATH_2010__348_3-4_235_0
Ciprian Foias; Ricardo M.S. Rosa; Roger Temam. A note on statistical solutions of the three-dimensional Navier–Stokes equations: The time-dependent case. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 235-240. doi : 10.1016/j.crma.2009.12.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.017/
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[6] C. Foias, R. Rosa, R. Temam, Properties of time-dependent statistical solutions of the three-dimensional Navier–Stokes equations, in preparation
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