Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations

TL;DR

This paper develops and analyzes estimators for the viscosity parameter in a stochastically perturbed 2D Navier-Stokes system, focusing on their consistency and asymptotic properties based on Fourier mode observations.

Contribution

It introduces new classes of estimators for the viscosity parameter and studies their statistical properties in stochastic Navier-Stokes equations.

Findings

Establishes consistency of the proposed estimators.

Proves asymptotic normality of the estimators.

Validates the methods for both periodic and bounded domains.

Abstract

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.