We consider elastic material exposed to compressible gas flow. First,
the problem is formulated using the comp. NS equations
in Eulerian coordinates and the equation of linear elasticity in Lagrangian
coordinates (as usual in fluid dynamics and
linear elasticity).
Then the problem is entirely written in Lagrangian coordinates and the
coupling condition is derived from an energy estimate.
The argument leads to uniqueness w.r.t. appropriate function spaces.
Still, the existence is an open problem.
There will be coffee and cake before the talk.