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In many occurrences of fluid-structure interaction time-periodic motions areobserved. We consider the interaction between a fluid driven by the threedimensional Navier-Stokes equation and a two dimensional linearized elasticKoiter shell situated at the boundary. The fluid-domain is a part of thesolution and as such changing in time periodically. On a steady part of theboundary we allow for the physically relevant case of dynamic pressure boundaryvalues, prominent to model inflow/outflow. We provide the existence of at leastone weak time-periodic solution for given periodic external forces that are nottoo large. For that we introduce new approximation techniques and a-prioriestimates.

Time-periodic weak solutions for the interaction of an incompressible  fluid with a linear Koiter type shell under dynamic pressure boundary  conditions