Limiting Behavior for an Iterated Viscosity

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 iter...

Full description

Saved in:
Bibliographic Details
Published in:ESAIM: Mathematical Modelling and Numerical Analysis 2000-03, Vol.34 (2), p.353-376
Main Authors: Foias, Ciprian, Jolly, Michael S., Manley, Oscar P.
Format: Article
Language:English
Subjects:
35Q30
37L65
Exact sciences and technology
Mathematical analysis
Mathematics
Navier-Stokes
Ordinary differential equations
Partial differential equations
Sciences and techniques of general use
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 dynamical system which displays several unusual mathematical features.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an:2000145