Compressible Fluids Interacting with a Linear-Elastic Shell

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies gamma > 12/7 (gamma > 1 in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Ruzicka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.