In the talk we address a system of PDEs describing an
interaction between an incompressible fluid and an elastic
body. The fluid motion is modeled by the Navier-Stokes
equations while an elastic body evolves according to an
linear elasticity equation. On the common boundary, the
velocities and stresses are matched. We discuss available
results on local well-posedness and prove new existence and
uniqueness results with the velocity and the displacement
belonging to low regularity spaces.

The results are joint with A. Tuffaha.