Observations on the vanishing viscosity limit

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...

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Published in:Transactions of the American Mathematical Society 2017-03, Vol.369 (3), p.2003-2027
Main Author: KELLIHER, JAMES P.
Format: Article
Language:English
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Summary: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 from these two papers.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6700