  We consider an viscous, incompressible Newtonian fluid flowing through a thin
elastic structure. The motion of the structure is described by the equations of
a linearised Koiter shell, whose motion is restricted to transverse
displacements. The fluid and the structure are coupled by the continuity of
velocities and an equilibrium of surface forces on the interface between fluid
and structure. On a fixed in- and outflow region we prescribe natural boundary
conditions. We show that weak solutions exist as long as the shell does not
self-intersect.
