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

Autor:	Hachicha, Imène
Rok vydání:	2013
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	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 homog\`enes des syst\`emes diff\'erentiels paraboliques et du syst\`eme 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. Comment: 29 pages, submitted to CPDE
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1308.0542 Zobrazit plný text záznamu View this record from Arxiv