Abstract

In this paper, we study a direct integral decomposition for the spaces L-2(O) and H-1(O) based on (xi, Y*)-periodic functions. Using this decomposition we can write the Green's operator ( associated to the classical Stokes system in fluid mechanics) in terms of a family of self-adjoint compact operators which depend on the parameter xi. As a consequence, we obtain the so-called Bloch waves associated to the Stokes system in the case of a periodic perforated domain.