LAUSR

Abstract We study the behavior of the longitudinal flow along a periodic array of cylinders upon perturbations of the shape of the cross section of the cylinders and the periodicity structure, when a Newtonian fluid is flowing at low Reynolds numbers around the cylinders. The periodicity cell is a rectangle of sides of length l and 1 / l , where l is a positive parameter, and the shape of the cross section of the cylinders is determined by the image of a fixed domain through a diffeomorphism ϕ. We also assume that the pressure gradient is parallel to the cylinders. Under such assumptions, for each pair ( l , ϕ ) , one defines the average of the longitudinal component of the flow velocity Σ [ l , ϕ ] . Here, we prove that the quantity Σ [ l , ϕ ] depends analytically on the pair ( l , ϕ ) , which we consider as a point in a suitable Banach space.