Stable determination of an immersed body in a stationary Stokes fluid

TL;DR

This paper addresses the inverse problem of identifying an immersed body within a stationary Stokes fluid using boundary measurements, providing a stability estimate of log-log type.

Contribution

It introduces a stability estimate for the inverse detection problem in a Stokes fluid, advancing understanding of the problem's ill-posedness.

Findings

Establishes a log-log type stability estimate.

Provides a theoretical framework for inverse detection in Stokes flows.

Enhances the mathematical understanding of fluid-structure inverse 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 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.