Size estimates of an obstacle in a stationary Stokes fluid

TL;DR

This paper develops bounds for estimating the size of an obstacle in a viscous fluid governed by the Stokes system using boundary measurements, advancing inverse problem techniques in fluid dynamics.

Contribution

It introduces new quantitative bounds for obstacle size estimation in Stokes flows based on boundary data, utilizing interior regularity and unique continuation estimates.

Findings

Established lower and upper bounds for obstacle size

Derived bounds depend on differences in boundary measurements

Applied regularity and unique continuation techniques

Abstract

In this work we are interested in estimating the size of a cavity D immersed in a bounded domain \Omega, contained in R^d, d=2,3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary of \Omega. More precisely, we establish some lower and upper bounds in terms of the difference between the external measurements when the obstacle is present and without the object. The proof of the result is based on interior regularity results and quantitative estimates of unique continuation for the solution of the Stokes system.