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Limiting Behavior for an Iterated Viscosity

Published online by Cambridge University Press:  15 April 2002

Ciprian Foias ,
Michael S. Jolly  and
Oscar P. Manley
Michael S. Jolly
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA. ([email protected])
Oscar P. Manley
Affiliation:
Gaithersburg, MD, 20878, USA.
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Abstract

The behavior of an ordinary differential equation for the low wave number velocitymode is analyzed. This equation was derived in [5]by an iterative process on the two-dimensional Navier-Stokes equations (NSE). Itresembles the NSE in form, exceptthat the kinematic viscosity is replaced by an iterated viscositywhich is a partial sum, dependent on the low-mode velocity. The convergence of this sum as the number of iterations is taken to be arbitrarily large is explored.This leads to a limiting dynamical system which displaysseveral unusual mathematical features.

Keywords

Navier-Stokes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 353 - 376
Copyright
© EDP Sciences, SMAI, 2000

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