Long-time behaviour of solutions to a nonlinear system of fluid-structure interaction

We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid. We prove local existence of strong solutions and global existence and uniqueness for small data. The main result is the characterization of long-time behaviour of the elastic displacement. We show convergence either to a rest state or rigid motion, or to a time-periodic pressure wave that may occur only in specific geometric settings.
Comment: 39 pages, 1 figure