Recovering discontinuous viscosity coefficients for inverse Stokes problems by boundary measurements

TL;DR

This paper proves that the discontinuous viscosity coefficient in a 3D Stokes problem can be uniquely identified from boundary measurements by analyzing Green's functions and constructing a coupled Stokes-Brinkman system.

Contribution

It introduces a novel approach combining Green's function analysis and a coupled Stokes-Brinkman system to achieve global uniqueness in inverse viscosity problems.

Findings

Unique determination of discontinuous viscosity from boundary data

Analysis of Green's function singularities in $H^1$-norm

Construction of a coupled Stokes-Brinkman system

Abstract

In this paper, we investigate the inverse Stokes problem of determining a discontinuous viscosity coefficient $\mu$ in a bounded domain $\Omega\subset\mathbb{R}^3$. By analyzing the singularity of the Dirichlet Green's functions in $H^1$-norm and constructing a specifically coupled Stokes-Brinkman system in a localized domain, we prove a global uniqueness theorem that the viscosity coefficient $\mu$ can be uniquely determined from boundary measurements.