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 (with respect to the viscosity), while for Besicovitch solutions certain limitations on the generalised Fourier coeﬃcients are requested.
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