## On a relaxation approximation of the incompressible Navier-Stokes equations

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- by Yann Brenier, Roberto Natalini and Marjolaine Puel
- Proc. Amer. Math. Soc.
**132**(2004), 1021-1028 - DOI: https://doi.org/10.1090/S0002-9939-03-07230-7
- Published electronically: November 14, 2003
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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.## References

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## Bibliographic 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