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We study a nonlinear coupled fluid–structure system modelling the blood flow through arteries. The fluid is described by the incompressible Navier–Stokes equations in a 2D rectangular domain where the upper part depends on a structure satisfying a damped Euler–Bernoulli beam equation. The system is driven by time-periodic source terms on the inflow and outflow boundaries. We prove the existence of time-periodic strong solutions for this problem under smallness assumptions for the source terms.

Existence of time-periodic strong solutions to a fluid–structure system