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On a relaxation approximation of the incompressible Navier-Stokes equations

Authors: Yann Brenier, Roberto Natalini and Marjolaine Puel
Journal: Proc. Amer. Math. Soc. 132 (2004), 1021-1028
MSC (2000): Primary 35Q30; Secondary 76D05
Published electronically: November 14, 2003
MathSciNet review: 2045417
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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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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

Roberto Natalini
Affiliation: Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy

Marjolaine Puel
Affiliation: Université Pierre et Marie Curie, Laboratoire d’analyse numérique, Boite courrier 187, F–75252 Paris cedex 05, France

Keywords: Incompressible Navier-Stokes equations, relaxation approximations, hyperbolic singular perturbations, modulated energy method
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
Article copyright: © Copyright 2003 American Mathematical Society