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On the inviscid limit of the Navier-Stokes equations


Authors: Peter Constantin, Igor Kukavica and Vlad Vicol
Journal: Proc. Amer. Math. Soc. 143 (2015), 3075-3090
MSC (2010): Primary 35Q35, 35Q30, 76D09
Published electronically: March 4, 2015
MathSciNet review: 3336632
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Abstract: We consider the convergence in the $ L^2$ norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow, and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer, then the inviscid limit holds.


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Additional Information

Peter Constantin
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: const@math.princeton.edu

Igor Kukavica
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: kukavica@usc.edu

Vlad Vicol
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: vvicol@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12638-X
Keywords: Inviscid limit, Navier-Stokes equations, Euler equations, boundary layer
Received by editor(s): March 23, 2014
Received by editor(s) in revised form: March 30, 2014
Published electronically: March 4, 2015
Communicated by: Catherine Sulem
Article copyright: © Copyright 2015 American Mathematical Society