Small Alfvén number limit for incompressible magneto-hydrodynamics in a domain with boundaries

for any fixed Alfvén number, the local well-posedness is proved for the equations of three-dimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth solution is shown to exist in a time interval independent of the Alfvén number, and the solutions of the original system tend to the solutions of a two-dimensional Euler flow coupled with a linear transport equation as the Alfvén number goes to zero.