Direct integral decomposition for periodic function spaces and application to Bloch waves

Abstract

In this paper, we study a direct integral decomposition for the spaces L2(O) and H1(O) based on (ξ 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 ξ. As a consequence, we obtain the so-called Bloch waves associated to the Stokes system in the case of a periodic perforated domain. © American Institute of Mathematical Sciences.