Small Alfvén number limit for shallow water magnetohydrodynamics

Qiangchang Ju, Jiawei Wang*, Xin Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Small Alfvén number limit of the shallow water magnetohydrodynamic equations with ill-prepared initial data is proved by applying fast averaging method. It is rigorously justified that the solutions of the original system tend to the solution of a one-dimensional system coupled with a linear system as the Alfvén number goes to zero. The approach is also used to study the small Alfvén number limit of the three-dimensional ideal incompressible magnetohydrodynamic equations.

Original languageEnglish
Article number127773
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Mar 2024
Externally publishedYes


  • Incompressible magnetohydrodynamic equations
  • Shallow water magnetohydrodynamic equations
  • Small Alfv́en number


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