Data Assimilation to the Primitive Equations with $L^p$-$L^q$-based Maximal Regularity Approach

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2024-01-04 DOI:10.1007/s00021-023-00843-2

Ken Furukawa

引用次数: 0

Abstract

In this paper, we show a mathematical justification of the data assimilation of nudging type in $L^p$-$L^q$ maximal regularity settings. We prove that the approximate solution of the primitive equations constructed by the data assimilation converges to the true solution with exponential order in the Besov space $B^{2/q}_{q,p}(\Omega )$ for $1/p + 1/q \le 1$ on the periodic layer domain $\Omega = \mathbb {T}^2 \times (-h, 0)$.

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采用基于 $$L^p$$ - $$L^q$$ 的最大正则性方法对原始方程进行数据同化

在本文中，我们展示了在$L^p$-$L^q$最大正则性设置中推导型数据同化的数学理由。我们证明，在周期层域 $\Omega = \mathbb {T}^2 \times (-h, 0)$上，数据同化所构造的原始方程的近似解在贝索夫空间 $B^{2/q}_{q,p}(\Omega )$ 中以指数阶收敛到真解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.

Data Assimilation to the Primitive Equations with \(L^p\)-\(L^q\)-based Maximal Regularity Approach

Abstract