Global existence and uniqueness of solutions to the equations of third grade fluids

We consider the limit alpha --> 0 for the equation of the second grade fluids. We prove that weak convergence of the solutions to a weak solution of the Navier-Stokes equation holds under the assumption that the initial data weakly converges in L-2. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.