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

Roger Lewandowski 1, 2, *
* Corresponding author
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
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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Roger Lewandowski. Navier-Stokes equations in the whole space with an eddy viscosity. Journal of Mathematical Analysis and Applications, Elsevier, 2019, 478 (2), pp.698-742. ⟨10.1016/j.jmaa.2019.05.051⟩. ⟨hal-01531260⟩

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