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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the inviscid limit of the Navier-Stokes equations
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by Peter Constantin, Igor Kukavica and Vlad Vicol PDF
Proc. Amer. Math. Soc. 143 (2015), 3075-3090 Request permission

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.
References
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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
  • MR Author ID: 314775
  • Email: kukavica@usc.edu
  • Vlad Vicol
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 846012
  • ORCID: setImmediate$0.00243841196800898$2
  • Email: vvicol@math.princeton.edu
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3075-3090
  • MSC (2010): Primary 35Q35, 35Q30, 76D09
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12638-X
  • MathSciNet review: 3336632