WEAK SOLUTIONS AND SINGULAR LIMITS FOR A COMPRESSIBLE FLUID-STRUCTURE INTERACTION PROBLEM WITH SLIP BOUNDARY CONDITIONS\ast

Abstract

We study a system describing the compressible barotropic fluids interacting with (visco-) elastic solid shell/plate. In particular, the elastic structure is part of the moving boundary of the fluid, and the Navier-slip type boundary condition is taken into account. Depending on the reference geometry (flat or not), we show the existence of weak solutions to the coupled system pro-vided the adiabatic exponent satisfies \gamma >12 7without damping and\gamma >3 with structure damping, 2 utilizing the domain extension and regularization approximation. Moreover, via a modified relative entropy method in time-dependent domains, 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. As a byproduct, with a fixed Reynolds number, we derive the incompressible limit without extra assump-tion. To the best of our knowledge, this is the first result concerning the singular limit problem for compressible fluids interacting with elastic structures. � 2026, Society for Industrial and Applied Mathematics Publications. All rights reserved.