Recovering discontinuous viscosity coefficients for inverse Stokes problems by boundary measurements

In this paper, we investigate the inverse Stokes problem of determining a discontinuous viscosity coefficient $\mu$ in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^3$. 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.