Asymptotics and stability for global solutions to the Navier-Stokes equations

Isabelle Gallagher[1]; Dragos Iftimie[2]; Fabrice Planchon[3]

  • [1] École Polytechnique, Centre de Mathématiques, UMR 7640, 91128 Palaiseau (France)
  • [2] Université de Rennes 1, IRMAR, UMR 6625, Campus de Beaulieu, 35042 Rennes (France)
  • [3] Université Paris 13, Institut Galilée, Laboratoire d’Analyse, Géométrie & Applications, UMR 7539, avenue J.-B. Clément, 93430 Villetaneuse (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 5, page 1387-1424
  • ISSN: 0373-0956

Abstract

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We consider an a priori global strong solution to the Navier-Stokes equations. We prove it behaves like a small solution for large time. Combining this asymptotics with uniqueness and averaging in time properties, we obtain the stability of such a global solution.

How to cite

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Gallagher, Isabelle, Iftimie, Dragos, and Planchon, Fabrice. "Asymptotics and stability for global solutions to the Navier-Stokes equations." Annales de l’institut Fourier 53.5 (2003): 1387-1424. <http://eudml.org/doc/116076>.

@article{Gallagher2003,
abstract = {We consider an a priori global strong solution to the Navier-Stokes equations. We prove it behaves like a small solution for large time. Combining this asymptotics with uniqueness and averaging in time properties, we obtain the stability of such a global solution.},
affiliation = {École Polytechnique, Centre de Mathématiques, UMR 7640, 91128 Palaiseau (France); Université de Rennes 1, IRMAR, UMR 6625, Campus de Beaulieu, 35042 Rennes (France); Université Paris 13, Institut Galilée, Laboratoire d’Analyse, Géométrie & Applications, UMR 7539, avenue J.-B. Clément, 93430 Villetaneuse (France)},
author = {Gallagher, Isabelle, Iftimie, Dragos, Planchon, Fabrice},
journal = {Annales de l’institut Fourier},
keywords = {Navier-Stokes equations; large time asymptotics; stability; infinite energy weak solutions; strong solutions; paradifferential calculus},
language = {eng},
number = {5},
pages = {1387-1424},
publisher = {Association des Annales de l'Institut Fourier},
title = {Asymptotics and stability for global solutions to the Navier-Stokes equations},
url = {http://eudml.org/doc/116076},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Gallagher, Isabelle
AU - Iftimie, Dragos
AU - Planchon, Fabrice
TI - Asymptotics and stability for global solutions to the Navier-Stokes equations
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 5
SP - 1387
EP - 1424
AB - We consider an a priori global strong solution to the Navier-Stokes equations. We prove it behaves like a small solution for large time. Combining this asymptotics with uniqueness and averaging in time properties, we obtain the stability of such a global solution.
LA - eng
KW - Navier-Stokes equations; large time asymptotics; stability; infinite energy weak solutions; strong solutions; paradifferential calculus
UR - http://eudml.org/doc/116076
ER -

References

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