Large time behavior to the system of incompressible non-Newtonian fluids in R2 ✩

In this paper, the authors study the large time behavior for the weak solutions to a class system of the incompressible non-Newtonian fluids in R2. It is proved that the weak solutions decay in L2 norm at (1+t)−1/2 and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation.  2004 Elsevier Inc. All rights reserved