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Asymptotically stable attracting sets in the Navier-Stokes equations

Published online by Cambridge University Press:  17 April 2009

P. E. Kloeden
P. E. Kloeden
Affiliation:
School of Mathematics and Physical Sciences, Murdoch University, Murdoch 6150, Western Australia.
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Abstract

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The planar Navier-Stokes equations with periodic boundary conditions are shown to have a nearby asymptotically stable attracting set whenever a Galerkin approximation involving the eigenfunctions of the Stokes operator has such an attracting set, provided the approximation has sufficiently many terms and its attracting set is sufficiently strongly stable. Lyapunov functions are used to characterize the stability of these attracting sets, which are compact sets of arbitrary geometric shape. This generalizes earlier results of Constantin, Foias and Temam and of the author for asymptotically stable steady solutions in the Navier-Stokes equations and such Galerkin approximations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 1 , August 1986 , pp. 37 - 52
Copyright
Copyright © Australian Mathematical Society 1986

References

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