In this talk, I will present a recent project concerning a system describing the compressible barotropic fluids interacting with (visco) elastic solid shell/plate with the Navier-slip type boundary condition. Depending on the reference geometry (flat or not), we show the existence of weak solutions to the coupled system in different situations. Particularly, we give a rigorous justification of the incompressible inviscid limit of the compressible fluid-structure interaction problem with a flat reference geometry, in the regime of low Mach number, high Reynolds number, and well-prepared initial data. This is based on the joint work with Sourav Mitra (IIT Indore) and Šárka Nečasová (IMCAS).
