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arXiv · 2310.17252

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

Yongqing Zhao·Wenjun Liu·Guangying Lv·Yuepeng Wang
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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 $H^2$-strong solution of the assimilation system converges exponentially to the reference solution in the sense of $L^2$ as $t\rightarrow \infty$. 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.

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Yongqing Zhao, Wenjun Liu, Guangying Lv, Yuepeng Wang. 2023-10-26. Continuous data assimilation for the three dimensional primitive equations with magnetic field. https://arxiv.org/abs/2310.17252

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