Carleman estimate for the Navier-Stokes equations and applications

TL;DR

This paper develops a Carleman estimate for linearized Navier-Stokes equations with applications to stability in inverse problems and source identification, advancing mathematical tools for fluid dynamics analysis.

Contribution

It introduces a new Carleman estimate with a regular weight function and applies it to establish stability results for inverse source problems in Navier-Stokes equations.

Findings

Established conditional stability for the lateral Cauchy problem.

Proved stability estimates for inverse source identification.

Extended mathematical techniques for fluid dynamics inverse problems.

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 inverse source problem of determining a spatially varying divergence-free factor of a source term.