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

Roger Lewandowski (1, 2)

1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Key-words: Navier-Stokes equations; eddy viscosities; turbulent solutions

Domaines: Equations aux dérivées partielles [math.AP]

Roger Lewandowski. Navier-Stokes equations in the whole space with an eddy viscosity. Journal of Mathematical Analysis and Applications, 2019, 478 (2), pp.698-742. ⟨10.1016/j.jmaa.2019.05.051⟩. ⟨hal-01531260⟩