Recovering the Parameter $\hat{I}\pm$ in the Simplified Bardina Model through Continuous Data Assimilation

Abstract

In this study, we develop a continuous data assimilation algorithm to recover the parameter $\hat{I}\pm$ in the simplified Bardina model. Our method utilizes the observations of finitely many Fourier modes by using a nudging framework that involves recursive parameter updates. We provide a rigorous convergence analysis, showing that the approximate parameter approaches the true value under suitable conditions, while the approximate solution also converges to the true solution.