Conditonal Lipschitz stability for the Inverse Problem of the 2D Navier-Stokes System in a Bounded Domain
Analysis of PDEs
2026-04-29 v1 Mathematical Physics
math.MP
Abstract
This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary conditions, and a global vorticity invariant constraint. We establish conditional Lipschitz stability and a local recovery for this inverse problem, where the velocity field and space-independent boundary vorticity are locally recovered from the given initial velocity field and the global vorticity invariant. Our analysis is based on well-posedness estimates and energy methods for the vorticity transport equation.
Cite
@article{arxiv.2604.25528,
title = {Conditonal Lipschitz stability for the Inverse Problem of the 2D Navier-Stokes System in a Bounded Domain},
author = {Jishan Fan and Yu Jiang and Sei Nagayasu and Gen Nakamura},
journal= {arXiv preprint arXiv:2604.25528},
year = {2026}
}