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Observations on the vanishing viscosity limit


Author: James P. Kelliher
Journal: Trans. Amer. Math. Soc. 369 (2017), 2003-2027
MSC (2010): Primary 76D05, 76B99, 76D10
DOI: https://doi.org/10.1090/tran/6700
Published electronically: June 2, 2016
MathSciNet review: 3581225
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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 from these two papers.


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Additional Information

James P. Kelliher
Affiliation: Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, California 92521
Email: kelliher@math.ucr.edu

DOI: https://doi.org/10.1090/tran/6700
Keywords: Vanishing viscosity, boundary layer theory
Received by editor(s): September 25, 2014
Received by editor(s) in revised form: March 16, 2015
Published electronically: June 2, 2016
Article copyright: © Copyright 2016 American Mathematical Society