Continuous data assimilation for the 3D primitive equations of the ocean

TL;DR

This paper demonstrates that continuous data assimilation effectively converges to the true solution of the 3D ocean primitive equations, ensuring exponential convergence and global existence of solutions.

Contribution

It proves the validity of continuous data assimilation for the 3D ocean primitive equations, including convergence and existence results.

Findings

Exponential convergence of assimilated solution to reference solution.

Global existence of strong solutions for the assimilated system.

Validation of data assimilation for complex ocean models.

Abstract

In this article, we show that the continuous data assimilation algorithm is valid for the 3D primitive equations of the ocean. Namely, the $L^2$ norm of the assimilated solution converge to that of the reference solution at an exponential rate in time. We also prove the global existence of strong solution to the assimilated system.