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Limiting behavior for an iterated viscosity

Ciprian Foias; Michael S. Jolly; Oscar P. Manley — 2000

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Limiting Behavior for an Iterated Viscosity

Ciprian Foias; Michael S. Jolly; Oscar P. Manley — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

The behavior of an ordinary differential equation for the low wave number velocity mode is analyzed. This equation was derived in [5] by an iterative process on the two-dimensional Navier-Stokes equations (NSE). It resembles the NSE in form, except that the kinematic viscosity is replaced by an iterated viscosity which 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...

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