Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations

We consider a parameter estimation problem to determine the viscosity $\nu$ of a stochastically perturbed 2D Navier-Stokes system. We derive several different classes of estimators based on the first $N$ Fourier modes of a single sample path observed on a finite time interval. We study the consistency and asymptotic normality of these estimators. Our analysis treats strong, pathwise solutions for both the periodic and bounded domain cases in the presence of an additive white (in time) noise.