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

2021/10/14 by Sergiy Zhuk, Zhuk, Sergiy, Mykhaylo Zayats +3 · 3 citations
Computer Science · Engineering · Mathematics · #76B75 #93C20 (Primary) 35Q30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2110.07738

openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H¹-sensitivity of NSE to small perturbations of initial conditions, yet the observer converges for known and uncertain inputs.

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