On the identifiability of a rigid body moving in a stationary viscous fluid

Carlos Conca (1) , Erica Schwindt (1, 2, 3) , Takéo Takahashi (2, 3)

1 DIM - Departamento de Ingeniería Matemática [Santiago]
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECN - Institut Élie Cartan de Nancy

This paper is devoted to a geometrical inverse problem associated with a fluid-structure system. More precisely, we consider the interaction between a moving rigid body and a viscous and incompressible fluid. Assuming a low Reynolds regime, the inertial forces can be neglected and, therefore, the fluid motion is modelled by the Stokes system. We first prove the well posedness of the corresponding system. Then we show an identifiability result: with one measure of the Cauchy forces of the fluid on one given part of the boundary and at some positive time, the shape of a convex body and its initial position are identified.

Domaines: Automatique

Carlos Conca, Erica Schwindt, Takéo Takahashi. On the identifiability of a rigid body moving in a stationary viscous fluid. Inverse Problems, 2012, 28 (1), pp.015005. ⟨10.1088/0266-5611/28/1/015005⟩. ⟨hal-00801908⟩