Detectability and global observer design for 2D Navier-Stokes equations with uncertain inputs

Sergiy Zhuk; Mykhaylo Zayats; Emilia Fridman

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arXiv · 2110.07738

Detectability and global observer design for 2D Navier-Stokes equations with uncertain inputs

Sergiy Zhuk·Mykhaylo Zayats·Emilia Fridman

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Abstract

We present simulation friendly detectability conditions for 2D Navier-Stokes Equation (NSE) with periodic boundary conditions, and describe a generic class of ``detectable'' observation operators: it includes pointwise evaluation of NSE's solution at interpolation nodes, and spatial average measurements. For ``detectable'' observation operators we design a global infinite-dimensional observer for NSE with uncertain possibly destabilizing inputs: in our numerical experiments we illustrate $H^1$-sensitivity of NSE to small perturbations of initial conditions, yet the observer converges for known and uncertain inputs.

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Sergiy Zhuk, Mykhaylo Zayats, Emilia Fridman. 2021-10-14. Detectability and global observer design for 2D Navier-Stokes equations with uncertain inputs. https://arxiv.org/abs/2110.07738

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