The enclosure method using a single point on the graph of the response operator for the Stokes system

TL;DR

This paper introduces a novel enclosure method for inverse obstacle problems governed by the Stokes system, utilizing only a single set of velocity and stress data over time to determine obstacle geometry.

Contribution

It presents two new extraction formulae based on the time domain enclosure method, requiring minimal data and providing a unified approach for the Stokes system.

Findings

Two types of extraction formulae are derived.

The method uses only velocity and stress data over finite time.

The approach effectively determines obstacle geometry.

Abstract

An inverse obstacle problem governed by the Stokes system in the time domain is considered. Two types of extraction formulae about the geometry of an unknown obstacle are given by using the most recent version of the time domain enclosure method in a unified style. Each of the formulae employs only a single set of velocity and the Cauchy stress fields over a finite time interval on the surface of the region where a viscous incompressible fluid occupies.