Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2

Details Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2 Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2

2001-02-26

arxiv.org/abs/math/0102197v1

Mathematics

Analysis of PDEs

46 pages, 3 figures

Scientific paper

10.1007/s002050200200

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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