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

TL;DR

This paper establishes global Lipschitz stability for an inverse source problem in linearized Navier-Stokes equations using Carleman estimates, enabling the determination of divergence-free sources from interior and boundary data.

Contribution

It introduces a novel stability result for inverse source problems in Navier-Stokes equations using Carleman estimates, which was not previously achieved.

Findings

Proved global Lipschitz stability for the inverse source problem.

Utilized Carleman estimates for Navier-Stokes and operator rot.

Achieved stability with interior data and velocity at a fixed time.

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 $t_0>0$ over the spatial domain. The key are Carleman estimates for the Navier-Stokes equations and the operator rot.