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In this work, we ask and answer the question: when is the viscosity of afluid uniquely determined from spatially sparse measurements of its velocityfield? We pose the question mathematically as an optimization problem using thedetermining map (the mapping of data to an approximation made via a nudgingalgorithm) to define a loss functional, the minimization of which solves theinverse problem of identifying the true viscosity given the measurement data.We give explicit a priori conditions for the well-posedness of this inverseproblem. In addition, we show that smallness of the loss functional impliesproximity to the true viscosity. We then present an algorithm for solving theinverse problem and prove its convergence.

Determining the viscosity of the Navier-Stokes equations from observations of finitely many modes