Time decay rates of non-Newtonian flows in [formula omitted

Abstract

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 L p − L q estimates, it is shown that the weak solutions decay in L 2 norm like t − n 2 ( 1 r − 1 2 ) when the initial velocity u 0 ∈ L 2 ∩ L r for 1 ⩽ r < 2 . The higher decay rates t − n 2 ( 1 r − 1 2 ) − 1 2 are obtained, if u 0 satisfies the additional moment condition ∫ R + n | x n u 0 ( x ) | r d x < ∞ , 1 < r ⩽ 2 . Moreover, the error estimates between the non-Newtonian flow and the Navier–Stokes flow are discussed.