On the detection of a moving obstacle in an ideal fluid by a boundary measurement

Abstract

In this paper, 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 centre of mass from a single boundary measurement. Linear stability estimates are also established by using shape differentiation techniques.