On the vanishing viscosity limit in a disk

We say that a solution of the Navier–Stokes equations converges in the vanishing viscosity limit to a solution of the Euler equations if their velocities converge in the energy ( L 2 ) norm uniformly in time as the viscosity ν vanishes. We show that a necessary and sufficient condition for the vanis...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische annalen 2009-03, Vol.343 (3), p.701-726
Main Author: Kelliher, James P.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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:We say that a solution of the Navier–Stokes equations converges in the vanishing viscosity limit to a solution of the Euler equations if their velocities converge in the energy ( L 2 ) norm uniformly in time as the viscosity ν vanishes. We show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the space–time energy density of the solution to the Navier–Stokes equations in a boundary layer of width proportional to ν vanish with ν , and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band centered around 1/ ν .
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-008-0287-3