  A mechanical interaction of compressible viscoelastic fluids with
viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order
(so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic
variant. The no-slip contact between fluid and solid is considered and the
Eulerian-frame return-mapping technique is used for both the fluid and the
solid models, which allows for a "monolithic" formulation of this
fluid-structure interaction problem. Existence and a certain regularity of weak
solutions is proved by a Schauder fixed-point argument combined with a suitable
regularization.
