The normal form of the Navier-Stokes equations in suitable normed spaces

Ciprian Foias; Luan Hoang; Eric Olson; Mohammed Ziane

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1635-1673
  • ISSN: 0294-1449

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Foias, Ciprian, et al. "The normal form of the Navier-Stokes equations in suitable normed spaces." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1635-1673. <http://eudml.org/doc/78907>.

@article{Foias2009,
author = {Foias, Ciprian, Hoang, Luan, Olson, Eric, Ziane, Mohammed},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Navier-Stokes; normal forms; normalization map; long time dynamics; asymptotic expansion},
language = {eng},
number = {5},
pages = {1635-1673},
publisher = {Elsevier},
title = {The normal form of the Navier-Stokes equations in suitable normed spaces},
url = {http://eudml.org/doc/78907},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Foias, Ciprian
AU - Hoang, Luan
AU - Olson, Eric
AU - Ziane, Mohammed
TI - The normal form of the Navier-Stokes equations in suitable normed spaces
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 5
SP - 1635
EP - 1673
LA - eng
KW - Navier-Stokes; normal forms; normalization map; long time dynamics; asymptotic expansion
UR - http://eudml.org/doc/78907
ER -

References

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  1. [1] Constantin P., Foias C., Navier–Stokes Equations, University of Chicago Press, Chicago, 1988. Zbl0687.35071MR972259
  2. [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. Zbl1109.76015MR2293465
  3. [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. Zbl1246.76019MR2225448
  4. [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. Zbl0994.35002MR1855030
  5. [5] Foias C., Saut J.C., Asymptotic behavior, as t + of solutions of Navier–Stokes equations and nonlinear spectral manifolds, Indiana Univ. Math. J.33 (3) (1984) 459-477. Zbl0565.35087MR740960
  6. [6] Foias C., Saut J.C., Linearization and normal form of the Navier–Stokes equations with potential forces, Ann. Inst H. Poincaré, Anal. Non Linéaire4 (1987) 1-47. Zbl0635.35075MR877990
  7. [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. Zbl0739.35066MR1101233
  8. [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. Zbl0454.35073MR544257
  9. [9] Foias C., Temam R., Gevrey class regularity for the solutions of the Navier–Stokes equations, J. Funct. Anal.87 (2) (1989) 359-369. Zbl0702.35203MR1026858
  10. [10] Guillope C., Remarques a propos du comportement lorsque t , des solutions des equations de Navier–Stokes associees a une force nulle, Bull. Soc. Math. France111 (1983) 151-180. Zbl0554.35098MR734218
  11. [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. Zbl0006.16702
  12. [12] Leray J., Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J. Math. Pures Appl.13 (1934) 331-418. Zbl60.0727.01JFM60.0727.01
  13. [13] Leray J., Essai sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math.63 (1934) 193-248. MR1555394JFM60.0726.05
  14. [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. Zbl0795.35082MR1256992

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