Time decay rates of non-Newtonian flows in R+n

This paper is concerned with time decay rates of the weak solutions of an incompressible non-Newtonian fluid motion model in half spaces R+n for n⩾3. With the use of the spectral decomposition of the Stokes operator and Lp−Lq estimates, it is shown that the weak solutions decay in L2 norm like t−n2(1r−12) when the initial velocity u0∈L2∩Lr for 1⩽r<2. The higher decay rates t−n2(1r−12)−12 are obtained, if u0 satisfies the additional moment condition∫R+n|xnu0(x)|rdx<∞,1