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

Jean Houot (1) , Jorge San Martin (1, 2) , Marius Tucsnak (1, 3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
3 IECN - Institut Élie Cartan de Nancy

In this paper, we study the motion of rigid bodies in a perfect incompressible fluid. The rigid-fluid system fils a bounded three dimensional domain. Adapting a strategy from Brezis and Bourguignon, 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.

Domaines: Equations aux dérivées partielles [math.AP]

Jean Houot, Jorge San Martin, Marius Tucsnak. Existence of solutions for the equations modeling the motion of rigid bodies in an ideal fluid. Journal of Functional Analysis, 2010, 259 (11), pp.2856-2885. ⟨10.1016/j.jfa.2010.07.006⟩. ⟨hal-00462366⟩