We consider an a priori global strong solution to the Navier-Stokes equations. We prove it behaves like a small solution for large time. Combining this asymptotics with uniqueness and averaging in time properties, we obtain the stability of such a global solution.
On considère une solution forte et globale des équations de Navier-Stokes. On montre qu'elle se comporte comme une solution petite en temps grand. En combinant ce résultat asymptotique avec des propriétés de moyenne en temps, on obtient la stabilité d'une telle solution globale.
Classification: 35B35, 35B40, 76D05
Keywords: Navier-Stokes equations, large time asymptotics, stability
@article{AIF_2003__53_5_1387_0, author = {Gallagher, Isabelle and Iftimie, Dragos and Planchon, Fabrice}, title = {Asymptotics and stability for global solutions to the {Navier-Stokes} equations}, journal = {Annales de l'Institut Fourier}, pages = {1387--1424}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {5}, year = {2003}, doi = {10.5802/aif.1983}, mrnumber = {2032938}, zbl = {1038.35054}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1983/} }
TY - JOUR TI - Asymptotics and stability for global solutions to the Navier-Stokes equations JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 1387 EP - 1424 VL - 53 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1983/ UR - https://www.ams.org/mathscinet-getitem?mr=2032938 UR - https://zbmath.org/?q=an%3A1038.35054 UR - https://doi.org/10.5802/aif.1983 DO - 10.5802/aif.1983 LA - en ID - AIF_2003__53_5_1387_0 ER -
%0 Journal Article %T Asymptotics and stability for global solutions to the Navier-Stokes equations %J Annales de l'Institut Fourier %D 2003 %P 1387-1424 %V 53 %N 5 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.1983 %R 10.5802/aif.1983 %G en %F AIF_2003__53_5_1387_0
Gallagher, Isabelle; Iftimie, Dragos; Planchon, Fabrice. Asymptotics and stability for global solutions to the Navier-Stokes equations. Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1387-1424. doi : 10.5802/aif.1983. https://aif.centre-mersenne.org/articles/10.5802/aif.1983/
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