Lipschitz stability estimate in the inverse Robin problem for the Stokes system

TL;DR

This paper establishes a Lipschitz stability estimate for recovering Robin coefficients on the boundary of a nonstationary Stokes system, under specific a priori assumptions, advancing inverse boundary value problem theory.

Contribution

It introduces a Lipschitz stability estimate for the inverse Robin problem in the Stokes system using an abstract framework, under finite-dimensional constraints.

Findings

Lipschitz stability estimate proved for Robin coefficient recovery

Applicable to nonstationary Stokes system with boundary data

Utilizes a theorem by L. Bourgeois for abstract inverse problems

Abstract

We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz stability estimate under the \textit{a priori} assumption that the Robin coefficient lives in some compact and convex subset of a finite dimensional vectorial subspace of the set of continuous functions. To do so, we use a theorem proved by L. Bourgeois which establishes Lipschitz stability estimates for a class of inverse problems in an abstract framework.