Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R2
Th. Gallay, C. E. Wayne
Abstract
We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R2 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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