Inverse problem for the geometric Navier-Stokes equations

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.