Global Lipschitz stability for an inverse source problem for the Navier–Stokes equations

Abstract

For linearized Navier–Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at over the spatial domain. The key machinery are Carleman estimates for the Navier–Stokes equations and the operator rot.