Time decay rates of non-Newtonian flows in Rn

This paper is concerned with time decay rates of the weak solutions of an incompressible non-Newtonian fluid motion model in half spaces Rn+ 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 ( 1 r −12 ) when the initial velocity u0 ∈ L2 ∩ Lr for 1 r < 2. The higher decay rates t−n2 ( 1 r −12 )−12 are obtained, if u0 satisfies the additional moment condition Rn+ xnu0(x) r dx <∞, 1 < r 2. Moreover, the error estimates between the non-Newtonian flow and the Navier–Stokes flow are discussed. © 2006 Elsevier Inc. All rights reserved.