Carleman estimate for the Navier–Stokes equations and applications. (1st August 2022)

• Record Type: Journal Article
• Authors: Imanuvilov, Oleg Y; Lorenzi, Luca; Yamamoto, Masahiro
• Is Part Of: Inverse problems. Volume 38:Number 8(2022)
• Publication Date: 2022-08-01
• Subjects: Navier–Stokes equations -- Carleman estimate -- inverse problem -- lateral Cauchy problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac4c33
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: For linearized Navier–Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauchy problem and finally we prove conditional stability estimates for the inverse source problem of determining a spatially varying divergence-free factor of a source term.