Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2 |
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| Authors: | Thierry Gallay C. Eugene Wayne |
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| Affiliation: | 1.Institut Fourier?Université de Grenoble I?F-38402 Saint-Martin d'Hères, France?e-mail: Thierry.gallay@ujf-grenoble.fr,FR;2.Department of Mathematics and Center for BioDynamics?Boston University, 111 Cummington Street?Boston, MA 02215, USA?e-mail: cew@math.bu.edu,US |
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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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