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Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes

Isabelle Gallagher; Dragoş Iftimie; Fabrice Planchon

Journées équations aux dérivées partielles (2002)

  • Volume: 334, Issue: 4, page 1-9
  • ISSN: 0752-0360

Abstract

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We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.

How to cite

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Gallagher, Isabelle, Iftimie, Dragoş, and Planchon, Fabrice. "Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes." Journées équations aux dérivées partielles 334.4 (2002): 1-9. <http://eudml.org/doc/93433>.

@article{Gallagher2002,
abstract = {We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.},
author = {Gallagher, Isabelle, Iftimie, Dragoş, Planchon, Fabrice},
journal = {Journées équations aux dérivées partielles},
keywords = {Cauchy problem; regularity; global solution; incompressible Navier-Stokes equations},
language = {eng},
number = {4},
pages = {1-9},
publisher = {Université de Nantes},
title = {Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes},
url = {http://eudml.org/doc/93433},
volume = {334},
year = {2002},
}

TY - JOUR
AU - Gallagher, Isabelle
AU - Iftimie, Dragoş
AU - Planchon, Fabrice
TI - Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes
JO - Journées équations aux dérivées partielles
PY - 2002
PB - Université de Nantes
VL - 334
IS - 4
SP - 1
EP - 9
AB - We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.
LA - eng
KW - Cauchy problem; regularity; global solution; incompressible Navier-Stokes equations
UR - http://eudml.org/doc/93433
ER -

References

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  2. [2] C. Calder´on. Existence of weak solutions for the Navier-Stokes equations with initial data in L p. Trans. Amer. Math. Soc., 318 (1), 179-200, 1990. Zbl0707.35118MR968416
  3. [3] M. Cannone. Ondelettes, paraproduits et Navier-Stokes, Diderotéditeur, Arts et Sciences, 1995. Zbl1049.35517MR1688096
  4. [4] J.-Y. Chemin and N. Lerner. Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes. J. Differential Equations, 121 (2), 314-328, 1995. Zbl0878.35089MR1354312
  5. [5] G. Furioli, P. Lemarié-Rieusset, and E. Terraneo. Unicité dans L 3 (R 3) et d'autres espaces fonctionnels limites pour Navier-Stokes. Rev. Mat. Iberoamericana, 16 (3), 605-667, 2000. Zbl0970.35101MR1813331
  6. [6] H. Fujita and T. Kato. On the Navier-Stokes initial value problem I, Archive for Rational Mechanics and Analysis, 16, 269-315, 1964. Zbl0126.42301MR166499
  7. [7] I. Gallagher, D. Iftimie and F. Planchon. Asymptotics and stability for global solutions to the Navier-Stokes equations. Preprint. Zbl1038.35054
  8. [8] I. Gallagher and F. Planchon. On global infinite energy solutions to the NavierStokes equations in two dimensions. Archive for Rational Mechanics and Analysis, 161, 307-337, 2002. Zbl1027.35090MR1891170
  9. [9] T. Kato. Strong L p solutions of the Navier-Stokes equations in R m with applications to weak solutions. Math. Zeit. 187, 471-480, 1984. Zbl0545.35073MR760047
  10. [10] H. Koch and D. Tataru. Well-posedness for the Navier-Stokes equations. Adv. Math., 157 (1), 22-35, 2001. Zbl0972.35084MR1808843
  11. [11] J. Leray. Sur le mouvement d'un liquide visqueux remplissant l'espace. Acta Mathematica, 63, 193-248, 1934. JFM60.0726.05
  12. [12] F. Planchon. Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in R 3. Annales de l'Institut Henri Poincaré, 12, 319-336, 1996 Zbl0865.35101MR1395675

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