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Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2

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Abstract

We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R 2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows us to extend those results in a number of ways.

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Authors and Affiliations

  1. Institut Fourier¶Université de Grenoble I¶F-38402 Saint-Martin d'Hères, France¶e-mail: Thierry.gallay@ujf-grenoble.fr, , , , , , FR

    Thierry Gallay

  2. Department of Mathematics and Center for BioDynamics¶Boston University, 111 Cummington Street¶Boston, MA 02215, USA¶e-mail: cew@math.bu.edu, , , , , , US

    C. Eugene Wayne

Authors
  1. Thierry Gallay
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  2. C. Eugene Wayne
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Accepted January 18, 2002¶Published online May 22, 2002

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Gallay, T., Wayne, C. Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2. Arch. Rational Mech. Anal. 163, 209–258 (2002). https://doi.org/10.1007/s002050200200

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  • DOI: https://doi.org/10.1007/s002050200200

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