Small Alfven number limit for shallow water magnetohydrodynamics

Small Alfven 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 Alfven number goes to zero. The approach is also used to study the small Alfven number limit of the three-dimensional ideal incompressible magnetohydrodynamic equations.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

The shallow water magnetohydrodynamic equations with ill-prepared initial data in the small Alfven number limit are proven to converge to the solution of a one-dimensional system coupled with a linear system using the fast averaging method. This method is also applied to study the small Alfven number limit of the three-dimensional ideal incompressible magnetohydrodynamic equations.