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

Abstract

We present $\textit{simulation friendly}$ 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.