Abstract
In this paper, we prove in two dimensions the global identifiability of the viscosity in an incompressible fluid by making boundary measurements. The main contribution of this work is to use more natural boundary measurements, the Cauchy forces, than the Dirichlet-to-Neumann map previously considered in Imanuvilov and Yamamoto (Global uniqueness in inverse boundary value problems for Navier–Stokes equations and Lamé ststem in two dimensions. arXiv:1309.1694, 2013) to prove the uniqueness of the viscosity for the Stokes equations and for the Navier–Stokes equations.
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Communicated by F. Lin
Ru-Yu Lai and Gunther Uhlmann were supported in part by the National Science Foundation. Gunther Uhlmann was also supported by a Simons Fellowship.
Jenn-Nan Wang was supported in part by MOST 102-2115-M-002-009-MY3.
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Lai, RY., Uhlmann, G. & Wang, JN. Inverse Boundary Value Problem for the Stokes and the Navier–Stokes Equations in the Plane. Arch Rational Mech Anal 215, 811–829 (2015). https://doi.org/10.1007/s00205-014-0794-1
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DOI: https://doi.org/10.1007/s00205-014-0794-1