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 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.