Asymptotics and stability for global solutions to the Navier-Stokes equations
Annales de l'Institut Fourier, Volume 53 (2003) no. 5, p. 1387-1424

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.

DOI : https://doi.org/10.5802/aif.1983
Classification:  35B35,  35B40,  76D05
Keywords: Navier-Stokes equations, large time asymptotics, stability 
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     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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {5},
     year = {2003},
     pages = {1387-1424},
     doi = {10.5802/aif.1983},
     zbl = {1038.35054},
     mrnumber = {2032938},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_2003__53_5_1387_0/

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