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On a relaxation approximation of the incompressible Navier-Stokes equations
Author(s):
Yann
Brenier;
Roberto
Natalini;
Marjolaine
Puel
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1021-1028.
MSC (2000):
Primary 35Q30;
Secondary 76D05
Posted:
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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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
DOI:
10.1090/S0002-9939-03-07230-7
PII:
S 0002-9939(03)07230-7
Keywords:
Incompressible Navier-Stokes equations,
relaxation approximations,
hyperbolic singular perturbations,
modulated energy method
Received by editor(s):
October 17, 2002
Posted:
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 of article:
Copyright
2003,
American Mathematical Society
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