Effect of hyperviscosity on the Navier-Stokes turbulence

Abdelhafid Younsi (1)

1 LAMNEDP - Laboratoire d'Analyse Mathématique et Numérique des Equations aux Dérivées Partielles

In this paper we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the conventional system as the regularization parameter goes to zero, for each dimension d $\le$ 4. Then we show that the use of this artificial viscosity term leads to truncated the number of degrees of freedom in the long-time behavior of the solutions to these equations. This result suggests that the hyperviscous Navier-Stokes system is an interesting model for three-dimensional fluid turbulence.

Mots clés: Navier-Stokes equations; Hyperviscosity; Weak solutions; Attractor dimension; Turbulence models

Domaines: Equations aux dérivées partielles [math.AP]

Abdelhafid Younsi. Effect of hyperviscosity on the Navier-Stokes turbulence. Electronic Journal of Differential Equations, 2010, 2010 (110), pp.19. ⟨hal-00459978v2⟩