01-75 Th. Gallay (Paris XI) and C.E. Wayne (Boston University)

Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on $R^2$ (232K, Postscript) Feb 24, 01

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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 one to extend those results in a number of ways.

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