arXiv:1409.7716 Abstract | arXiv Analytics

arXiv:1409.7716 [math.AP]Abstract References Reviews Resources

Observations on the vanishing viscosity limit

Published 2014-09-26Version 1

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.

Categories: math.AP

Subjects: 76D05, 76B99, 76D10

Keywords: vanishing viscosity limit, observations, navier-stokes equations converge, euler equations, vortex sheet

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