The Normal Form of the Navier-Stokes Equations in Suitable Normed Spaces

Foias, Ciprian; Hoang, Luan; Olson, Eric; Ziane, Mohammed

Foias, Ciprian ; Hoang, Luan ; Olson, Eric ; Ziane, Mohammed

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 1635-1673 / Harvested from Numdam

Access to full text
Full (PDF)
Full (DJVU)

Publié le : 2009-01-01

MR 2566704 | Zbl 1179.35212

DOI : https://doi.org/10.1016/j.anihpc.2008.09.003

@article{AIHPC_2009__26_5_1635_0,
     author = {Foia\c s, Ciprian and Hoang, Luan and Olson, Eric and Ziane, Mohammed},
     title = {The Normal Form of the Navier-Stokes Equations in Suitable Normed Spaces},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {1635-1673},
     doi = {10.1016/j.anihpc.2008.09.003},
     mrnumber = {2566704},
     zbl = {1179.35212},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_5_1635_0}
}

Foias, Ciprian; Hoang, Luan; Olson, Eric; Ziane, Mohammed. The Normal Form of the Navier-Stokes Equations in Suitable Normed Spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 1635-1673. doi : 10.1016/j.anihpc.2008.09.003. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_5_1635_0/

Bibliographie

[1] Constantin P., Foias C., Navier-Stokes Equations, University of Chicago Press, Chicago, 1988. | MR 972259 | Zbl 0687.35071

[2] Foias C., Hoang L., Nicolaenko B., On the Helicity in 3D-Periodic Navier-Stokes Equations I: the Nonstatistical Case, Proc. London Math. Soc. (3) 94 (2007) 53-90. | MR 2293465 | Zbl 1109.76015

[3] Foias C., Hoang L., Olson E., Ziane M., On the Solutions to the Normal Form of the Navier-Stokes Equations, Indiana Univ. Math. J. 55 (2) (2006) 631-686. | MR 2225448 | Zbl pre05034338

[4] Foias C., Manley O., Rosa R., Temam R., Navier-Stokes Equations and Turbulence, Encyclopedia of Mathematics and its Applications, vol. 83, Cambridge University Press, Cambridge, 2001. | MR 1855030 | Zbl 0994.35002

[5] Foias C., Saut J. C., Asymptotic Behavior, as $t \to + \infty$ of Solutions of Navier-Stokes Equations and Nonlinear Spectral Manifolds, Indiana Univ. Math. J. 33 (3) (1984) 459-477. | MR 740960 | Zbl 0565.35087

[6] Foias C., Saut J. C., Linearization and Normal Form of the Navier-Stokes Equations With Potential Forces, Ann. Inst H. Poincaré, Anal. Non Linéaire 4 (1987) 1-47. | Numdam | MR 877990 | Zbl 0635.35075

[7] Foias C., Saut J. C., Asymptotic Integration of Navier-Stokes Equations With Potential Forces. I, Indiana Univ. Math. J. 40 (1) (1991) 305-320. | MR 1101233 | Zbl 0739.35066

[8] Foias C., Temam R., Some Analytic and Geometric Properties of Solutions of the Evolution Navier-Stokes Equations, J. Math. Pures Appl. 58 (3) (1979) 334-368. | MR 544257 | Zbl 0454.35073

[9] Foias C., Temam R., Gevrey Class Regularity for the Solutions of the Navier-Stokes Equations, J. Funct. Anal. 87 (2) (1989) 359-369. | MR 1026858 | Zbl 0702.35203

[10] Guillope C., Remarques a Propos Du Comportement Lorsque $t \to \infty$ , Des Solutions Des Equations De Navier-Stokes Associees a Une Force Nulle, Bull. Soc. Math. France 111 (1983) 151-180. | Numdam | MR 734218 | Zbl 0554.35098

[11] Leray J., Etude De Diverse Equations Integrales Non Lineares Et De Quelques Problemes Que Pose L'hydrodynamique, J. Math. Pures Appl. 12 (1933) 1-82. | Zbl 0006.16702

[12] Leray J., Essai Sur Les Mouvements Plans D'un Liquide Visqueux Que Limitent Des Parois, J. Math. Pures Appl. 13 (1934) 331-418. | JFM 60.0727.01

[13] Leray J., Essai Sur Le Mouvement D'un Liquide Visqueux Emplissant L'espace, Acta Math. 63 (1934) 193-248. | JFM 60.0726.05 | MR 1555394

[14] Ponce G., Racke R., Sideris T. C., Titi E. S., Global Stability of Large Solutions to the 3D Navier-Stokes Equations, Commun. Math. Phys. 159 (1994) 329-341. | MR 1256992 | Zbl 0795.35082