## Behavior of a rigid body in an incompressible viscous fluid near a boundary.(English)Zbl 1060.76038

Colli, Pierluigi (ed.) et al., Free boundary problems: theory and applications. Proceedings of a conference, Trento, Italy, June 2002. Basel: Birkhäuser (ISBN 3-7643-2193-8/hbk). ISNM, Int. Ser. Numer. Math. 147, 313-327 (2003).
The paper deals with the motion of a rigid body in a viscous incompressible fluid in the 2-D and 3-D cases. Let $$\Omega$$ be a domain in $$\mathbb R^n$$ $$(n=2,3)$$ occupied by an incompressible fluid. $$S$$ is a rigid body. $$S$$ is moving into $$\Omega$$, $$S\subset\Omega$$. The author investigates the situations related to the contacts of the body $$S$$ with the boundary of $$\Omega$$. The motion of the body during and before the contact is studied. Sufficient conditions which yield the impossibility of the collisions are formulated. An example showing that the weak solutions of the problem admit collisions of the body $$S$$ with $$\partial\Omega$$ is constructed too.
For the entire collection see [Zbl 1027.00020].

### MSC:

 76D99 Incompressible viscous fluids 35Q35 PDEs in connection with fluid mechanics

### Keywords:

rigid body; viscous fluid; collision