Stable determination of a body immersed in a fluid: the nonlinear stationary case

TL;DR

This paper addresses the inverse problem of identifying a submerged body in a fluid governed by stationary Navier-Stokes equations, providing a stability estimate based on boundary measurements.

Contribution

It introduces a stability estimate of log-log type for the inverse problem of detecting a body in a fluid using boundary data.

Findings

Stability estimate of log-log type established

Single boundary measurement suffices for detection

Theoretical framework for inverse fluid-structure problems

Abstract

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier-Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log-log type.