On the motion and collisions of rigid bodies in an ideal fluid

Jean-Gabriel Houot (1) , Alexandre Munnier (1)

1 CORIDA - Robust control of infinite dimensional systems and applications

In this paper we study a coupled system of partial differential equations and ordinary differential equations. This system is a model for the 3d interactive free motion of rigid bodies immersed in an ideal fluid. Applying the least action principle of Lagrangian mechanics, we prove that the solids degrees of freedom solve a second order system of nonlinear ordinary differential equations. Under suitable smoothness assumptions on the solids and on the fluid's domain boundaries, we prove the existence and $C^\infty$ regularity, up to a collision between two solids or between a solid with the boundary of the fluid domain, of the solids motion. The case of an infinite cylinder surrounded by a fluid occupying an half space is tackled. By a careful asymptotic analysis of a Neumann PDE, when the distance between the cylinder and the wall goes to zero, we prove that collisions with non zero relative velocity can occur.

Mots clés: fluid-solid interaction; ideal fluid; lagrangian mechanics; colisions; pde-ode coupled system

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Jean-Gabriel Houot, Alexandre Munnier. On the motion and collisions of rigid bodies in an ideal fluid. Asymptotic Analysis, 2008, 56 (3-4), pp.125-158. ⟨hal-00095617⟩