# Detectability and global observer design for Navier-Stokes equations with unknown inputs

@inproceedings{Zhuk2021DetectabilityAG, title={Detectability and global observer design for Navier-Stokes equations with unknown inputs}, author={Sergiy M. Zhuk and Mykhaylo Zayats and Emilia Fridman}, year={2021} }

We present easy-to-verify detectability conditions for Navier-Stokes Equation (NSE) in two spatial dimensions with periodic boundary conditions, and describe a generic class of “detectable” observation operators: it includes point-like measurements (e.g. pointwise evaluation of NSE’s solution at interpolation nodes), and spatial average measurements. For “detectable” observation operators we design a global observer for NSE with unknown possibly destabilizing inputs: in our numerical…

## One Citation

Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks

- Computer ScienceArXiv
- 2022

By running a set of numerical experiments, it is demonstrated that the proposed network does recover unknown forcing from data and is capable of predicting turbulent ﬂows in high resolution from low resolution noisy observations.

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