Appears in collection : Jean-Morlet Chair 2022 - Conference: Nonlinear PDEs in Fluid Dynamics / Chaire Jean-Morlet 2022 - Conférence : EDP non-linéaires en dynamique des fluides

We address a system of partial differential equations modeling a motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the wave equation. We will review the local for large and global existence theorems and present the most most recent global existence result, which is joint with A. Tuffaha and W. Ozanski.