  In this paper, we are interested in the error estimates of the reiterated
Stokes systems in a bounded $C^{1,1}$ domain with Dirichlet boundary
conditions. And we have obtained the $O(\varepsilon)$ error estimates for the
velocity term and $O(\varepsilon^{1/2})$ error estimates for the pressure term.
Compared to the general homogenization of Stokes systems problems, the
difficulty in the reiterated homogenization is that we need to handle the
different scales of $x$. To overcome this difficulty, we use the Fourier
transform methods which was firstly introduced by the author in [10] to
separate these different scales. We also note that this method may be adapted
to a more general multi-scale homogenization problem.
