Recovering discontinuous viscosity coefficients for inverse Stokes problems by boundary measurements

Abstract

In this paper, we investigate the inverse Stokes problem of determining a discontinuous viscosity coefficient $\hat{I}¼$ in a bounded domain $\hat{I}\text{c◯}\subset {\mathbb{R}}^3$. 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 $\hat{I}¼$ can be uniquely determined from boundary measurements.