Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain
[Comportement asymptotique en temps des solutions de l’équation de Navier-Stokes dans un domaine extérieur du plan]
Gallay, Thierry
Journées équations aux dérivées partielles, (2012), p. 1-17 / Harvested from Numdam
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Nous étudions le comportement asymptotique en temps des solutions de l’équation de Navier-Stokes incompressible dans un domaine extérieur du plan, avec condition de non-glissement à la frontière. Les données initiales que nous considérons sont des perturbations d’énergie finie d’un tourbillon régulier dont la circulation à l’infini est petite, mais nous n’imposons aucune autre restriction à leur taille. En utilisant une estimation d’énergie logarithmique et des arguments d’interpolation, nous montrons que la solution converge lorsque t→∞ vers un tourbillon d’Oseen autosimilaire. Ce résultat a été obtenu en collaboration avec Y. Maekawa (Université de Kobe).

We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as t→∞. This result was obtained in collaboration with Y. Maekawa (Kobe University).

Publié le : 2012-01-01
DOI : https://doi.org/10.5802/jedp.86
Classification:  35Q30,  35B35,  76D05,  76D17
Mots clés: Equation de Navier-Stokes, comportement asymptotique, domaine extérieur 
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     title = {Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2012},
     pages = {1-17},
     doi = {10.5802/jedp.86},
     language = {en},
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Gallay, Thierry. Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain. Journées équations aux dérivées partielles,  (2012), pp. 1-17. doi : 10.5802/jedp.86. http://gdmltest.u-ga.fr/item/JEDP_2012____A3_0/

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