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arXiv · 1308.0542

A finite speed of propagation approximation for the incompressible Navier-Stokes equations

Imène Hachicha
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Abstract

In this paper, we introduce a finite propagation speed perturbation of the incompressible Navier-Stokes equations (NS). The model we consider is inspired by a hyperbolic perturbation of the heat equation due to Cattaneo (Sulla conduzione del calore. Atti Semin. Mat. Fis. Univ., Modena, 1949, 3:83-101) and by an equation that Vishik and Fursikov (Solutions statistiques homogènes des systèmes différentiels paraboliques et du système de Navier-Stokes. Ann. Scuola Norm. Sup. Pisa Cl. Sci., 1977, 4:531-576) investigated in order to find statistical solutions to (NS). We prove that the solutions to the perturbed Navier-Stokes equation approximate those to (NS). We use refined energy methods involving fractional Sobolev spaces and precise estimates on the nonlinear term due to the dyadic Littlewood-Paley decomposition.

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Imène Hachicha. 2013-08-02. A finite speed of propagation approximation for the incompressible Navier-Stokes equations. https://arxiv.org/abs/1308.0542

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