Wellposedness and Stability Results for the Navier-Stokes Equations in 𝐑 3
Chemin, Jean-Yves ; Gallagher, Isabelle
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 599-624 / Harvested from Numdam
@article{AIHPC_2009__26_2_599_0,
     author = {Chemin, Jean-Yves and Gallagher, Isabelle},
     title = {Wellposedness and Stability Results for the Navier-Stokes Equations in $\mathbf {R}^3$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {599-624},
     doi = {10.1016/j.anihpc.2007.05.008},
     mrnumber = {2504045},
     zbl = {1165.35038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_2_599_0}
}
Chemin, Jean-Yves; Gallagher, Isabelle. Wellposedness and Stability Results for the Navier-Stokes Equations in $\mathbf {R}^3$. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 599-624. doi : 10.1016/j.anihpc.2007.05.008. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_2_599_0/

[1] Auscher P., Dubois S., Tchamitchian P., On the Stability of Global Solutions to Navier-Stokes Equations in the Space, Journal de Mathématiaques Pures et Appliquées 83 (2004) 673-697. | MR 2062638 | Zbl 1107.35096

[2] Bahouri H., Chemin J.-Y., Gallagher I., Refined Hardy Inequalities, Annali di Scuola Normale di Pisa, Classe di Scienze, Serie V 5 (2006) 375-391. | Numdam | MR 2274784 | Zbl 1121.43006

[3] Bahouri H., Gérard P., High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations, American Journal of Mathematics 121 (1999) 131-175. | MR 1705001 | Zbl 0919.35089

[4] M. Cannone, Y. Meyer, F. Planchon, Solutions autosimilaires des équations de Navier-Stokes, Séminaire “Équations aux Dérivées Partielles” de l'École polytechnique, Exposé VIII, 1993-1994. | Numdam | MR 1300903 | Zbl 0882.35090

[5] Chemin J.-Y., Fluides Parfaits Incompressibles, Astérisque, vol. 230, 1995, English translation: J.-Y. Chemin, Perfect Incompressible Fluids, Oxford University Press, 1998. | MR 1340046 | Zbl 0829.76003

[6] Chemin J.-Y., Théorèmes D'unicité Pour Le Système De Navier-Stokes Tridimensionnel, Journal d'Analyse Mathématique 77 (1999) 27-50. | MR 1753481 | Zbl 0938.35125

[7] J.-Y. Chemin, Localization in Fourier space and Navier-Stokes system, in: Phase Space Analysis of Partial Differential Equations, Proceedings 2004, CRM series, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Normale di Pisa, pp. 53-136. | MR 2144406 | Zbl 1081.35074

[8] Chemin J.-Y., Gallagher I., On the Global Wellposedness of the 3-D Navier-Stokes Equations With Large Initial Data, Annales Scientifiques de l'École Normale Supérieure de Paris 39 (4) (2006) 679-698. | Numdam | MR 2290141 | Zbl 1124.35052

[9] Foias C., Saut J.-C., Asymptotic Behaviour, as t, of Solutions of the Navier-Stokes Equations and Nonlinear Spectral Manifolds, Indiana Mathematical Journal 33 (3) (1984) 459-477. | MR 740960 | Zbl 0565.35087

[10] Fujita H., Kato T., On the Navier-Stokes Initial Value Problem I, Archive for Rational Mechanics and Analysis 16 (1964) 269-315. | MR 166499 | Zbl 0126.42301

[11] Gallagher I., The Tridimensional Navier-Stokes Equations With Almost Bidimensional Data: Stability, Uniqueness and Life Span, International Mathematical Research Notices 18 (1997) 919-935. | MR 1481611 | Zbl 0893.35098

[12] Gallagher I., Profile Decomposition for the Navier-Stokes Equations, Bulletin de la Société Mathématique de France 129 (2001) 285-316. | Numdam | MR 1871299 | Zbl 0987.35120

[13] Gallagher I., Iftimie D., Planchon F., Asymptotics and Stability for Global Solutions to the Navier-Stokes Equations, Annales de l'Institut Fourier 53 (5) (2003) 1387-1424. | Numdam | MR 2032938 | Zbl 1038.35054

[14] Gérard P., Description Du Défaut De Compacité De L'injection De Sobolev, ESAIM Contrôle Optimal et Calcul des Variations 3 (1998) 213-233. | Numdam | MR 1632171 | Zbl 0907.46027

[15] Giga Y., Miyakawa T., Solutions in L r of the Navier-Stokes Initial Value Problem, Archive for Rational Mechanics and Analysis 89 (3) (1985) 267-281. | MR 786550 | Zbl 0587.35078

[16] Iftimie D., The 3D Navier-Stokes Equations Seen as a Perturbation of the 2D Navier-Stokes Equations, Bulletin de la Société Mathématique de France 127 (1999) 473-517. | Numdam | MR 1765551 | Zbl 0946.35059

[17] Kato T., Strong L p Solutions of the Navier-Stokes Equations in R m With Applications to Weak Solutions, Mathematische Zeitschrift 187 (1984) 471-480. | MR 760047 | Zbl 0545.35073

[18] Koch H., Tataru D., Well-Posedness for the Navier-Stokes Equations, Advances in Mathematics 157 (2001) 22-35. | MR 1808843 | Zbl 0972.35084

[19] Ladyzhenskaya O., The Mathematical Theory of Viscous Incompressible Flow, Mathematics and its Applications, vol. 2, Second English edition, revised and enlarged, Gordon and Breach, Science Publishers, New York-London-Paris, 1969, xviii+224 pp. | MR 254401 | Zbl 0184.52603

[20] Leibovich S., Mahalov A., Titi E., Invariant Helical Subspaces for the Navier-Stokes Equations, Archive for Rational Mechanics and Analysis 112 (3) (1990) 193-222. | MR 1076072 | Zbl 0708.76044

[21] Lemarié-Rieusset P.-G., Recent Developments in the Navier-Stokes Problem, Research Notes in Mathematics, vol. 431, Chapman & Hall/CRC, 2002. | MR 1938147 | Zbl 1034.35093

[22] Leray J., Essai Sur Le Mouvement D'un Liquide Visqueux Emplissant L'espace, Acta Matematica 63 (1933) 193-248. | JFM 60.0726.05 | MR 124922

[23] Ponce G., Racke R., Sideris T., Titi E., Global Stability of Large Solutions to the 3D Navier-Stokes Equations, Communitacions in Mathematical Physics 159 (1994). | MR 1256992 | Zbl 0795.35082

[24] Ukhovskii M., Iudovich V., Axially Symmetric Flows of Ideal and Viscous Fluids Filling the Whole Space, Prikladnaya Matematika i Mekhanika 32 (1968) 59-69, (in Russian); translated as, Journal of Applied Mathematics and Mechanics 32 (1968) 52-61. | MR 239293 | Zbl 0172.53405