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arXiv · 1409.7716

Observations on the vanishing viscosity limit

James P. Kelliher
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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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James P. Kelliher. 2014-09-26. Observations on the vanishing viscosity limit. https://arxiv.org/abs/1409.7716

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