Continuous data assimilation for the three dimensional primitive equations with magnetic field

Article type: Research Article

Authors: Zhao, Yongqing^a | Liu, Wenjun^{a; b; *} | Lv, Guangying^{a; b} | Wang, Yuepeng^{a; b}

Affiliations: [a] School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China | [b] Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing 210044, China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the H2-strong solution of the assimilation system converges exponentially to the reference solution in the sense of L2 as t→∞. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity equation.

Keywords: Well-posedness, data assimilation, sensitivity analysis

DOI: 10.3233/ASY-241912

Journal: Asymptotic Analysis, vol. 140, no. 1-2, pp. 77-108, 2024