On s’intéresse aux propriétés de décroissance temporelle pour les dérivées des solutions globales à énergie finie des équations de Navier–Stokes dans des domaines généraux bidimensionnels. Les estimations obtenues ne dépendent que de l’ordre de dérivation et de la norme des données initiales. La même méthode élémentaire basée sur les bornes d’énergie et l’inégalité de Ladyzhenskaya conduit également à des résultats de régularité Gevrey.
The present paper is devoted to the proof of time decay estimates for derivatives at any order of finite energy global solutions of the Navier–Stokes equations in general two-dimensional domains. These estimates only depend on the order of derivation and on the norm of the initial data. The same elementary method just based on energy estimates and Ladyzhenskaya inequality also leads to Gevrey regularity results.
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Raphaël Danchin 1
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@article{AFST_2024_6_33_5_1215_0,
author = {Rapha\"el Danchin},
title = {On the decay and {Gevrey} regularity of the solutions to the {Navier{\textendash}Stokes} equations in general two-dimensional domains},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1215--1232},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 33},
number = {5},
year = {2024},
doi = {10.5802/afst.1797},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1797/}
}
TY - JOUR AU - Raphaël Danchin TI - On the decay and Gevrey regularity of the solutions to the Navier–Stokes equations in general two-dimensional domains JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2024 SP - 1215 EP - 1232 VL - 33 IS - 5 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1797/ DO - 10.5802/afst.1797 LA - en ID - AFST_2024_6_33_5_1215_0 ER -
%0 Journal Article %A Raphaël Danchin %T On the decay and Gevrey regularity of the solutions to the Navier–Stokes equations in general two-dimensional domains %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2024 %P 1215-1232 %V 33 %N 5 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1797/ %R 10.5802/afst.1797 %G en %F AFST_2024_6_33_5_1215_0
Raphaël Danchin. On the decay and Gevrey regularity of the solutions to the Navier–Stokes equations in general two-dimensional domains. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 5, pp. 1215-1232. doi : 10.5802/afst.1797. https://afst.centre-mersenne.org/articles/10.5802/afst.1797/
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