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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 a relaxation approximation of the incompressible Navier-Stokes equations
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by Yann Brenier, Roberto Natalini and Marjolaine Puel PDF
Proc. Amer. Math. Soc. 132 (2004), 1021-1028 Request permission

Abstract:

We consider a hyperbolic singular perturbation of the incompressible Navier Stokes equations in two space dimensions. The approximating system under consideration arises as a diffusive rescaled version of a standard relaxation approximation for the incompressible Euler equations. The aim of this work is to give a rigorous justification of its asymptotic limit toward the Navier Stokes equations using the modulated energy method.
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Additional Information
  • Yann Brenier
  • Affiliation: Laboratoire J. A. Dieudonné, U.M.R. C.N.R.S. No. 6621, Université de Nice Sophia-Antipolis, Parc Valrose, F–06108 Nice, France
  • Email: brenier@math.unice.fr
  • Roberto Natalini
  • Affiliation: Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy
  • Email: rnatalini@iac.rm.cnr.it
  • Marjolaine Puel
  • Affiliation: Université Pierre et Marie Curie, Laboratoire d’analyse numérique, Boite courrier 187, F–75252 Paris cedex 05, France
  • Email: mpuel@ceremade.dauphine.fr
  • Received by editor(s): October 17, 2002
  • Published electronically: November 14, 2003
  • Additional Notes: Partially supported by European TMR projects NPPDE # ERB FMRX CT98 0201 and CNR Short Term Visiting program and European Union RTN HYKE Project: HPRN-CT-2002-00282
  • Communicated by: Suncica Canic
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1021-1028
  • MSC (2000): Primary 35Q30; Secondary 76D05
  • DOI: https://doi.org/10.1090/S0002-9939-03-07230-7
  • MathSciNet review: 2045417