On the W^{2,q}-regularity of incompressible fluids with shear-dependent viscosities: The shear-thinning case;

n this paper we improve the results stated in Reference [2], in this same Journal, by using -basically- the same tools. We consider a non Newtonian fluid governed by equations with p-structure and we show that second order derivatives of the velocity and first order derivatives of the pressure belong to suitable Lebesgue spaces