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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-04 DOI:10.1007/s00021-023-00843-2

Ken Furukawa

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引用次数: 0

摘要

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。

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

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.