Recovering discontinuous viscosity coefficients for inverse Stokes problems by boundary measurements

2025/11/24 by Jia, Yu, Wu, Chengyu, Wu, Hao +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.2511.18812

openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the inverse Stokes problem of determining a discontinuous viscosity coefficient μ in a bounded domain Ω⊂ℝ³. By analyzing the singularity of the Dirichlet Green's functions in H¹-norm and constructing a specifically coupled Stokes-Brinkman system in a localized domain, we prove a global uniqueness theorem that the viscosity coefficient μ can be uniquely determined from boundary measurements.

Citations

• Global uniqueness in inverse boundary value problems for Navier-Stokes equations and Lamé system in two dimensions
• The Calderón problem with partial data
• On uniqueness of recovery of a discontinuous conductivity coefficient
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Related

• Simultaneous Reconstruction of Multiple Unknowns in Stokes-Darcy System from Partial Boundary Data
• Determining the viscosity from the boundary information for incompressible fluid
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem
• The Stokes problem with Navier boundary conditions in irregular domains
• Well-posedness of the Stokes-transport system in bounded domains and in\n the infinite strip