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

We present simulation friendly detectability conditions for 2D Navier-Stokes Equation (NSE) with peri-odic 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.(c) 2023 Published by Elsevier Ltd.