Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in ℝ 3

F. Planchon

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 3, page 319-336
  • ISSN: 0294-1449

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Planchon, F.. "Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in $\mathbb {R}^3$." Annales de l'I.H.P. Analyse non linéaire 13.3 (1996): 319-336. <http://eudml.org/doc/78385>.

@article{Planchon1996,
author = {Planchon, F.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Besov space; heat kernel; paraproduct decomposition; Bernstein's lemma},
language = {eng},
number = {3},
pages = {319-336},
publisher = {Gauthier-Villars},
title = {Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/78385},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Planchon, F.
TI - Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in $\mathbb {R}^3$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 3
SP - 319
EP - 336
LA - eng
KW - Besov space; heat kernel; paraproduct decomposition; Bernstein's lemma
UR - http://eudml.org/doc/78385
ER -

References

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  2. [2] J. Bergh and J. Löfstrom, Interpolation Spaces, An Introduction, Springer-Verlag, 1976. Zbl0344.46071MR482275
  3. [3] J.M. Bony, Calcul symbolique et propagation des singularités dans les équations aux dérivées partielles non linéaires, Ann. Sci. Ecole Norm. Sup., Vol. 14, 1981, pp. 209-246. Zbl0495.35024MR631751
  4. [4] M. Cannone, Ondelettes, Paraproduits et Navier-Stokes, PhD thesis, Université Paris IX, CEREMADE F-75775 PARIS CEDEX, 1994, to be published by Diderot Editeurs (1995). MR1688096
  5. [5] J.-Y. Chemin, Remarques sur l'existence globale pour le système de Navier-Stokes incompressible, SIAM Journal Math. Anal., Vol. 23, 1992, pp. 20-28. Zbl0762.35063MR1145160
  6. [6] Y. Giga, Solutions for Semi-Linear Parabolic Equations in Lp and Regularity of Weak Solutions of the Navier-Stokes System, Journal of differential equations, Vol. 61, 1986, pp. 186-212. Zbl0577.35058
  7. [7] Y. Giga and T. Miyakawa, Solutions in Lr of the Navier-Stokes Initial Value Problem, Arch. Rat. Mech. Anal., Vol. 89, 1985, pp. 267-281. Zbl0587.35078MR786550
  8. [8] R. Kajikiya and T. Miyakawa, On L2 Decay of Weak Solutions of the Navier-Stokes Equations in Rn, Math. Zeit., Vol. 192, 1986, pp. 135-148. Zbl0607.35072MR835398
  9. [9] T. Kato, Strong Lp Solutions of the Navier-Stokes Equations in Rm with Applications to Weak Solutions, Math. Zeit., Vol. 187, 1984, pp. 471-480. Zbl0545.35073MR760047
  10. [10] T. Kato and H. Fujita, On the non-stationnary Navier-Stokes system, Rend. Sem. Math. Univ. Padova, Vol. 32, 1962, pp. 243-260. Zbl0114.05002MR142928
  11. [11] T. Kato and H. Fujita, On the Navier-Stokes Initial Value Problem I, Arch. Rat. Mech. Anal., Vol. 16, 1964, pp. 269-315. Zbl0126.42301MR166499
  12. [12] J. Peetre, New thoughts on Besov Spaces, Duke Univ. Math. Series, Duke University, Durham, 1976. Zbl0356.46038MR461123
  13. [13] J. Serrin, On the Interior Regularity of Weak Solutions of the Navier-Stokes Equations, Arch. Rat. Mech. Anal., Vol. 9, 1962, pp. 187-195. Zbl0106.18302MR136885
  14. [14] E.M. Stein, Singular Integral and Differentiability Properties of Functions, Princeton University Press, 1970. Zbl0207.13501MR290095
  15. [15] M. Taylor, Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations, Comm. in PDE, Vol. 17, 1992, pp. 1407-1456. Zbl0771.35047MR1187618
  16. [16] H. Triebel, Theory of Function Spaces, volume 78 of Monographs in Mathematics, Birkhauser, 1983. Zbl0546.46027MR730762

Citations in EuDML Documents

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  1. Isabelle Gallagher, Dragoş Iftimie, Fabrice Planchon, Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes
  2. Dragoş Iftimie, Equations de Navier-Stokes sur des domaines minces tridimensionnels et espaces anisotropes
  3. Isabelle Gallagher, Décomposition en profils pour les solutions des équations de Navier-Stokes
  4. Isabelle Gallagher, Profile decomposition for solutions of the Navier-Stokes equations
  5. Marius Paicu, Fluides incompressibles horizontalement visqueux
  6. Marco Cannone, Nombres de Reynolds, stabilité et Navier-Stokes

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