  We prove existence and uniqueness for fully-developed (Poiseuille-type) flows
in semi-infinite cylinders, in the setting of (time) almost-periodic functions.
In the case of Stepanov almost-periodic functions the proof is based on a
detailed variational analysis of a linear "inverse" problem, while in the
Besicovitch setting the proof follows by a precise analysis in wave-numbers.
  Next, we use our results to construct a unique almost periodic solution to
the so called "Leray's problem" concerning 3D fluid motion in two semi-infinite
cylinders connected by a bounded reservoir. In the case of Stepanov functions
we need a natural restriction on the size of the flux, while for Besicovitch
solutions certain limitations on the generalized Fourier coefficients are
requested.

Analysis of PDEs