Inverse boundary value problem for the Stokes and the Navier-Stokes equations in the plane

In this paper, we prove in two dimensions 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 \cite{IY} to prove the uniqueness of the viscosity for the Stokes equations and for the Navier-Stokes equations.