Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 695-714.doi: 10.1007/s10473-025-0223-6

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THREE-SCALE SINGULAR LIMITS OF THE MHD ROTATING SHALLOW WATER SYSTEM

Yue Fang1, Jiawei Wang2, Xin Xu1,*   

  1. 1. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China;
    2. Graduate School of China Academy of Engineering Physics, Beijing 100193, China
  • Received:2023-08-02 Revised:2024-03-18 Online:2025-03-25 Published:2025-05-08
  • Contact: *Xin Xu, E-mail: xx@ouc.edu.cn
  • About author:Yue Fang, E-mail: yyfang0929@163.com;Jiawei Wang, E-mail: wangjiawei19@gscaep.ac.cn
  • Supported by:
    Xu's research was supported by Natural Science Foundation of China(12001506) and the Natural Science Foundation of Shandong Province(ZR2020QA014).

Abstract: A mathematically rigorous framework for singular limits of the magnetohydrodynamic rotating shallow water equations with ill-prepared data is developed when the Rossby and Froude numbers tend to zero at different rates. The reduced systems are derived, respectively, for the stratification-dominant and the rotation-dominant cases by means of the developed three-scale fast averaging method.

Key words: three-scale singular limits, Rossby and Froude numbers, ill-prepared data

CLC Number: 

  • 76M45
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