Upper semicontinuity of trajectory attractors of 3D Navier-Stokes equations with hyperviscosity.

Abdelhafid Younsi (1)

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

We regularized the 3D Navier-Stokes equations by adding a fourth-order viscosity term. We study the upper semicontinuity, of the global attractors of the Leray-Hopf weak solutions of the regularized 3D Navier-Stokes equations, as the artificial dissipation goes to 0, and the regularized problem (see equation (1.1)) limits to the standard 3D Navier-Stokes equations. We also consider applications of obtained results to the regularized problem by allowing the family of forcing functions to vary with epsilon, for epsilon >0.

Mots clés: hyperviscosity; Navier Stokes equations; attractor; upper semicontinuity; hyperviscosity.

Domaines: Equations aux dérivées partielles [math.AP]

Abdelhafid Younsi. Upper semicontinuity of trajectory attractors of 3D Navier-Stokes equations with hyperviscosity.. 2009. ⟨hal-00442964v1⟩