Foundations of Fluid Dynamics pp 227-286 | Cite as

# Incipient Turbulence and Chaos

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## Abstract

Analysing the fundamental problems of the NS equation has, in particular, brought up clearly the lack of an adequate algorithm, i.e. convergent and constructive, for its solution. Furthermore even if we knew that the fluid equations had unique and regular solutions, for regular initial data (for the NS equation this is true if *d =* 2 and likely if *d =* 3, but false if *d >*4) this would not help much in the understanding of the physical properties of such solutions at large times.

## Keywords

Periodic Orbit Hopf Bifurcation Periodic Motion Rotation Number Period Doubling Bifurcation
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© Springer-Verlag Berlin Heidelberg 2002