Observations on the vanishing viscosity limit
Analysis of PDEs
2014-09-30 v1
Abstract
Whether, in the presence of a boundary, solutions of the Navier-Stokes equations converge to a solution to the Euler equations in the vanishing viscosity limit is unknown. In a seminal 1983 paper, Tosio Kato showed that the vanishing viscosity limit is equivalent to having sufficient control of the gradient of the Navier-Stokes velocity in a boundary layer of width proportional to the viscosity. In a 2008 paper, the present author showed that the vanishing viscosity limit is equivalent to the formation of a vortex sheet on the boundary. We present here several observations that follow on from these two papers.
Keywords
Cite
@article{arxiv.1409.7716,
title = {Observations on the vanishing viscosity limit},
author = {James P. Kelliher},
journal= {arXiv preprint arXiv:1409.7716},
year = {2014}
}