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On a relaxation approximation of the incompressible Navier-Stokes equations |
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| Authors: | Yann Brenier Roberto Natalini Marjolaine Puel |
| Institution: | Laboratoire J. A. Dieudonné, U.M.R. C.N.R.S. No. 6621, Université de Nice Sophia-Antipolis, Parc Valrose, F--06108 Nice, France ; Istituto per le Applicazioni del Calcolo ``Mauro Picone', Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy ; Université Pierre et Marie Curie, Laboratoire d'analyse numérique, Boite courrier 187, F--75252 Paris cedex 05, France |
| 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. |
| Keywords: | Incompressible Navier-Stokes equations relaxation approximations hyperbolic singular perturbations modulated energy method |
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