Abstract
Poiseuille flows in infinite cylindrical pipes, in spite of their enormous simplicity, have a main role in many theoretical and applied problems. As is well known, the Poiseuille flow is a stationary solution of the Stokes and the Navier-Stokes equations with a given constant flux. Time-periodic flows in channels and pipes have a comparable importance. However, the problem of the existence of time-periodic flows in correspondence to any given time-periodic total flux, is still an open problem. A solution is known only in some very particular cases, for instance, the Womersley flows. Our aim is to solve this problem in the general case. The above existence result opens the way to further investigations. As an example of this possibility we consider the extension of the classical Leray's problem for Poiseuille flows to arbitrary time-periodic flows.
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