Electronic Journal of Differential Equations, Vol. 2010(2010), No. 110, pp. 1-19. Title: Effect of hyperviscosity on the Navier-Stokes turbulence Author: Abdelhafid Younsi (USTHB, Algiers, Algeria) Submitted December 2, 2009. Published August 9, 2010. Math Subject Classifications: 76D05, 76F20, 35B30, 35B41, 35B65, 37L30, 37K40. Key Words: Navier-Stokes equations; hyperviscosity; weak solutions; attractor dimension; turbulence models