A dispersive approach to the artificial compressibility approximations of the Navier Stokes equations in 3-D

Details A dispersive approach to the artificial compressibility approximations of the Navier Stokes equations in 3-D A dispersive approach to the artificial compressibility approximations of the Navier Stokes equations in 3-D

2006-07-27

arxiv.org/abs/math/0607702v1

Mathematics

Analysis of PDEs

14 pages. to appear in Journal of Hyperbolic Differential Equations

Scientific paper

In this paper we study how to approximate the Leray weak solutions of the incompressible Navier Stokes equation. In particular we describe an hyperbolic version of the so called artificial compressibility method investigated by J.L.Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimate of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier Stokes equation.

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