On a relaxation approximation of the incompressible Navier-Stokes equations

Brenier, Yann; Natalini, Roberto; Puel, Marjolaine

doi:10.1090/S0002-9939-03-07230-7

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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