Incompressible non-Newtonian fluids: time asymptotic behaviour of weak solutions

We study the asymptotic behaviour in time of incompressible non-Newtonian fluids in the whole space assuming that initial data also belong to L1. Firstly, we consider the weak solution to the power-law model with non-zero external forces and we find the asymptotic behaviour in time of this solution in the same class of existence and uniqueness with p(greater than or equal to)11/5. Secondly, we are interested in the asymptotic behaviour of weak solutions to the second grade model, and finally, we deal with the asymptotic behaviour in time of weak solutions to a simplified model of viscoelastic fluids of the Oldroyd type.