Navier-Stokes equations in the whole space with an eddy viscosity

2017/05/31 by Roger Lewandowski, Lewandowski, Roger
Mathematics · #35D30 #35Q30 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35D30 #msc:35Q30 #msc:76D03 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1705.11043

arxiv created 2017/05/31 · arxiv updated 2017/06/01

Abstract

We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove that when the regularizing parameter goes to zero, the solution of the regularized system converges to a turbulent solution of the initial system.

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