Marius Tucsnak
Université de Bordeaux, Bordeaux, France

We consider systems describing the coupled motion of rigid bodies and viscous fluids. We discuss two situations. In the first case the solid is fully immersed in a 3D viscous fluid filling the remaining part of the space. In the second one, the solid undergoes vertical motion only and it is floating at the surface of a fluid described by the equations of viscous shallow water waves. In both cases, the main ingredient is the refined study of a newly introduced object, called the "fluid-structure semigroup".