Carleman estimate for the Navier-Stokes equations and applications

• Main Authors: Imanuvilov, O.Y (Author), Lorenzi, L. (Author), Yamamoto, M. (Author)
• Format: Article
• Language: English
• Published: Institute of Physics 2022
• Subjects: Carleman estimate; Cauchy problems; Conditional stability; Divergence free; inverse problem; Inverse problems; Inverse source problem; lateral Cauchy problem; Lateral cauchy problem; Linearized navier-stokes equations; Navier Stokes equations; Navier-Stokes equation; Navier-Stokes equations; Stability estimates; Viscous flow; Weight functions
• Online Access: View Fulltext in Publisher
• ISBN: 02665611 (ISSN)
• ISSN: 02665611 (ISSN)
• DOI: 10.1088/1361-6420/ac4c33

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. © 2022 IOP Publishing Ltd.