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

[摘要] 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) is an element of L-2 boolean AND L-r for 2 <= 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 integral(n)(R+) vertical bar x(n)u(0)(x)vertical bar(r)dx < infinity, 1 < r <= 2. Moreover, the error estimates between the non-Newtonian flow and the Navier-Stokes flow are discussed. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] L-2 decay;spectral decomposition;non-Newtonian flows