Asymptotic analysis of the navier-stokes equations

New bounds are established on the number of modes which determine the solutions of the Navier-Stokes equations in two dimensions. The best bound available at present is nearly proportional to the generalized Grashof number (defined in the paper), and less than logarithmically dependent on the spatia...

Full description

Saved in:
Bibliographic Details
Published in:Physica. D 1983-01, Vol.9 (1), p.157-188
Main Authors: Foias, C., Manley, O.P., Temam, R., Treve, Y.M.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Physics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:New bounds are established on the number of modes which determine the solutions of the Navier-Stokes equations in two dimensions. The best bound available at present is nearly proportional to the generalized Grashof number (defined in the paper), and less than logarithmically dependent on the spatial structure, or the shape of the force driving the flow. To the extent than for the case of 2-dimensional Rayleigh-Bénard convection, the generalized Grashof number may be identified with the usual Grashof number, the resulting bound on the number of modes is found to differ only slightly from a bound obtained earlier on heuristic grounds.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(83)90297-X