Time periodic solutions of the Navier-Stokes equations with the time periodic Poiseuille flow under (GOC) for a symmetric perturbed channel in R-2

摘要

Beirao da Veiga 5 proves that for a straight channel in R-n (n >= 2) and for a given time periodic flux there exists a unique time periodic Poiseuille flow. As a by product, existence of the time periodic Poiseuille flow in perturbed channels (Leray's problem) is shown for the Stokes problem (n >= 2) and for the Navier-Stokes problem (n <= 4). Concerning the Navier-Stokes case, in 5 a quantitative condition required to show the existence of the solutions depends not just on the flux of the time periodic Poiseuille flow but also on the domain itself.