Detecting a moving obstacle in an ideal fluid by a boundary measurement

Carlos Conca (1) , Patricio Cumsille (1) , Jaime Ortega (1) , Lionel Rosier (2)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 IECN - Institut Élie Cartan de Nancy

In this Note we investigate the problem of the detection of a moving obstacle in a perfect fluid occupying a bounded domain in R2 from the measurement of the velocity of the fluid on one part of the boundary. We show that when the obstacle is a ball, we may identify the position and the velocity of its center of mass from a single boundary measurement. Linear stability estimates are also established by using shape differentiation techniques.

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

Carlos Conca, Patricio Cumsille, Jaime Ortega, Lionel Rosier. Detecting a moving obstacle in an ideal fluid by a boundary measurement. Comptes Rendus. Mathématique, 2008, 346 (15-16), pp.839-844. ⟨10.1016/j.crma.2008.06.007⟩. ⟨hal-00600924⟩