Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell

Abstract

In this paper we analyse the interaction of an incompressible Newtonian fluid with a linearly elastic Koiter shell whosemotion is restricted to transverse displacements. The middle surface of the shell constitutes the mathematical boundary of the three-dimensional fluid domain. We show that weak solutions exist as long as the magnitude of the displacement stays below some (possibly large) bound that rules out selfintersections of the shell.