Global weak solutions for an incompressible Newtonian fluid interacting   with a linearly elastic Koiter shell
  In this paper we analyze the interaction of an incompressible Newtonian fluid with a linearly elastic Koiter shell whose motion is restricted to transverse displacements. The middle surface of the shell constitutes the mathematical boundary of the threedimensional fluid domain. We show that weak solutions exist as long as the magnitude of the displacement stays below some (possibly large) bound which is determined by the geometry of the undeformed shell. 
Daniel Lengeler, Michael Ruzicka
math.AP