Stability estimates for a Robin coefficient in the two-dimensional Stokes system

TL;DR

This paper investigates the inverse problem of determining a Robin boundary coefficient in the 2D Stokes system, establishing a logarithmic stability estimate under certain conditions using Carleman inequalities.

Contribution

It provides the first stability estimate for Robin coefficient identification in the 2D Stokes system with explicit conditions and a novel application of Carleman inequalities.

Findings

Proved identifiability of the Robin coefficient.

Established a logarithmic stability estimate.

Applied Carleman inequality to boundary inverse problems.

Abstract

In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first study the identifiability of the Robin coefficient and then we establish a stability estimate of logarithm type thanks to a Carleman inequality due to A. L. Bukhgeim and under the assumption that the velocity of a given reference solution stays far from 0 on a part of the boundary where Robin conditions are prescribed.