Inverse problem for the geometric Navier-Stokes equations
Analysis of PDEs
2026-02-10 v1
Abstract
We consider the inverse problem of determining a compact Riemannian manifold with boundary from fixed time observations of the solution, restricted to a small subset in space, for the Navier-Stokes system with a local source on the manifold. Our approach is based on a reduction to an inverse problem for an auxiliary hyperbolic Stokes system, via linearization and spectral techniques. We solve the resulting inverse problem by a new generalization of the Boundary Control method.
Cite
@article{arxiv.2602.08644,
title = {Inverse problem for the geometric Navier-Stokes equations},
author = {Yavar Kian and Lauri Oksanen and Ziyao Zhao},
journal= {arXiv preprint arXiv:2602.08644},
year = {2026}
}