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

Abstract

We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space IR 3 . 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. MCS Classification: 35Q30, 35D30, 76D03, 76D05.A(t, x)|∇u(t, x)| 2 dx 1 2 = || A(t, ·)∇u(t, ·)|| 0,2 .

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