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arXiv · 2602.08644

Inverse problem for the geometric Navier-Stokes equations

Yavar Kian·Lauri Oksanen·Ziyao Zhao
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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.

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Yavar Kian, Lauri Oksanen, Ziyao Zhao. 2026-02-09. Inverse problem for the geometric Navier-Stokes equations. https://arxiv.org/abs/2602.08644

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