In this talk, I will discuss the evolution of rigid bodies in a perfect incompressible fluid, and the limit systems that can be obtained as the bodies shrink to points. The model is as follows: the fluid is driven by the incompressible Euler equation, while the solids evolve according Newton’s equations under the pressure force on their boundary. We investigate the question of the limit of the system as (some of) the solids converge to a point while keeping a constant velocity circulation on their boundary. We obtain a complete picture when each solid can belong to either of the three categories:
— solids that have a fixed size,
— solids that shrink to a point while keeping a fixed mass,
— solids that shrink to a point and having mass going to zero.
In the limit, we obtain a system coupling the Euler equation for the fluid, Newton’s equations for the non-shrinking bodies, and massive/non-massive point vortices for the remaining ones.

This is a joint work with Franck Sueur (Bordeaux, France), following works with Christophe Lacave (Grenoble, France), Alexandre Munnier (Nancy, France) and Franck Sueur.