Data Assimilation to the Primitive Equations with Lp - Lq -based Maximal Regularity Approach

Ken Furukawa

doi:10.1007/s00021-023-00843-2

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

Ken Furukawa^*

^*Corresponding author for this work

Program of Mathematics and Informatics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 Bq,p2/q(Ω) for 1 / p+ 1 / q≤ 1 on the periodic layer domain Ω = T²× (- h, 0) .

Original language	English
Article number	9
Journal	Journal of Mathematical Fluid Mechanics
Volume	26
Issue number	1
DOIs	https://doi.org/10.1007/s00021-023-00843-2
State	Published - 2024/02

Keywords

Asymptotic analysis
Data assimilation
Maximal L - L regularity
The primitive equations

ASJC Scopus subject areas

Mathematical Physics
Condensed Matter Physics
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s00021-023-00843-2

Cite this

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abstract = "In this paper, we show a mathematical justification of the data assimilation of nudging type in Lp - Lq 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 Bq,p2/q(Ω) for 1 / p+ 1 / q≤ 1 on the periodic layer domain Ω = T2× (- h, 0) .",

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KW - The primitive equations

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