We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown viscosity. We determine the large-time error between the true solution of the 2 dimensional Navier--Stokes equations and the assimilated solution due to discrepancy between an approximate viscosity and the physical viscosity. Additionally, we develop an algorithm that can be run in tandem with the AOT algorithm to recover both the true solution and the true viscosity using only spatially discrete velocity measurements.
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Carlson et al. (2020) studied this question.
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