On the motion and collision of rigid bodies in an ideal fluid. (English) Zbl 1165.35300

Houot, Jean; Munnier, Alexandre

Asymptotic Anal. 56, No. 3-4, 125-158 (2008).

Summary: 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 degrees of freedom of the solids solve a system of second-order nonlinear ordinary differential equations. Under suitable smoothness assumptions on the fluid’s domain boundary we prove the existence and \(C^\infty\) regularity of the solids motion, up to a collision between two solids or between a solid with the boundary of the fluid’s domain. The case of an infinite cylinder surrounded by a fluid in a half space cavity is tackled. By a careful asymptotic analysis of a Neumann boundary value problem (solved by the fluid’s potential) when the distance between the cylinder and the wall goes to zero we prove that collisions with non zero relative velocity can occur.

MSC:

35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35Q35	PDEs in connection with fluid mechanics
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

PDE-ODE system; fluid-solid interaction; ideal fluid; Lagrangian mechanics; collisions; Neumann boundary value problem