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We consider the physical setup of a three-dimensional fluid-structureinteraction problem. A viscous compressible gas or liquid interacts with anonlinear, visco-elastic, three-dimensional bulk solid. The latter is describedby a hyperbolic evolution with a non-convex elastic energy functional. Thefluid is modelled by the compressible Navier--Stokes equations with abarotropic pressure law. Due to the motion of the solid, the fluid domain istime-changing. Our main result is the long-time existence of a weak solution tothe coupled system until the time of a collision. The nonlinear couplingbetween the motions of the two different matters is established via the methodof minimising movements. The motion of both the solid and the fluid is chosenvia an incrimental minimization with respect to dissipative and staticpotentials. These variational choices together with a careful construction ofan underlying flow map for our approximation then directly result in thepressure gradient and the material time derivatives.

Compressible fluids interacting with 3D visco-elastic bulk solids