Global uniqueness in inverse boundary value problems for the Navier–Stokes equations and Lamé system in two dimensions. (11th February 2015)

• Record Type: Journal Article
• Authors: Imanuvilov, O Yu; Yamamoto, M
• Is Part Of: Inverse problems. Volume 31:Number 3(2015:Mar.)
• Publication Date: 2015-02-11
• Subjects: Lamé system -- Navier–Stokes system -- Calderón problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/3/035004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider inverse boundary value problems for the Navier–Stokes equations and the isotropic Lamé system in two dimensions. The question of global uniqueness for these inverse problems, without any smallness assumptions on unknown coefficients, has been a longstanding open problem for the Navier–Stokes equations and the isotropic Lamé system in two dimensions. We prove the global uniqueness for both inverse boundary value problems. Our methodology is the same for both systems. The key is the construction of complex geometric optics solutions after decoupling the systems into weakly coupling systems.