Existence of solutions for the equations modeling the motion of rigid bodies in an ideal fluid

In this paper, we study the motion of rigid bodies in a perfect incompressible fluid. The rigid-fluid system fills a bounded domain in R3. Adapting the strategy from Bourguignon and Brezis (1974) [1], we use the stream lines of the fluid and we eliminate the pressure by solving a Neumann problem. In this way, the system is reduced to an ordinary differential equation on a closed infinite-dimensional manifold. Using this formulation, we prove the local in time existence and uniqueness of strong solutions.