Inverse Boundary Value Problem for the Stokes and the Navier–Stokes Equations in the Plane

Ru Yu Lai; Gunther Uhlmann; Jenn Nan Wang

doi:10.1007/s00205-014-0794-1

Inverse Boundary Value Problem for the Stokes and the Navier–Stokes Equations in the Plane

Ru Yu Lai, Gunther Uhlmann, Jenn Nan Wang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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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 arxiv.org/abs/1309.1694, 2013) to prove the uniqueness of the viscosity for the Stokes equations and for the Navier–Stokes equations.

Original language	English (US)
Pages (from-to)	811-829
Number of pages	19
Journal	Archive For Rational Mechanics And Analysis
Volume	215
Issue number	3
DOIs	https://doi.org/10.1007/s00205-014-0794-1
State	Published - Mar 2014

Bibliographical note

Funding Information:
Ru-Yu Lai and Gunther Uhlmann were supported in part by the National Science Foundation. Gunther Uhlmann was also supported by a Simons Fellowship.

Funding Information:
Jenn-Nan Wang was supported in part by MOST 102-2115-M-002-009-MY3.

Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

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10.1007/s00205-014-0794-1

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title = "Inverse Boundary Value Problem for the Stokes and the Navier–Stokes Equations in the Plane",

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 Lam{\'e} ststem in two dimensions. arXiv:1309.1694 arxiv.org/abs/1309.1694, 2013) to prove the uniqueness of the viscosity for the Stokes equations and for the Navier–Stokes equations.",

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Inverse Boundary Value Problem for the Stokes and the Navier–Stokes Equations in the Plane

Abstract

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