Observations on the vanishing viscosity limit

2014/09/26 by Kelliher, James P.
#76B99 #76D05 #76D10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.7716

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.

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