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