Parameter Recovery for the Three‐Dimensional Primitive Equations With Magnetic Field via Continuous Data Assimilation

In this paper, we investigate the parameter recovery within the Azouani–Olson–Titi (AOT) continuous data assimilation framework for the three‐dimensional (3D) primitive equations with magnetic field. We analyze the long‐time error between the reference and assimilation solutions, which arises from discrepancies in the unknown viscosity and magnetic diffusion coefficients. To address this, we propose a parameter recovery algorithm. While extending the framework originally developed for the 2D Navier–Stokes equations, our algorithm is tailored to handle the additional complexities of the 3D system, such as fluid–magnetic coupling and anisotropic structure. We rigorously prove the convergence of the proposed recovery algorithm under appropriate conditions.