INCOMPRESSIBLE LIMIT OF IDEAL MAGNETOHYDRODYNAMIC EQUATIONS WITH A PERFECTLY CONDUCTING WALL CONDITION

We study the incompressible limit of classical solutions to the compressible ideal magnetohydrodynamic equations in three-dimensional half space with a perfectly conducting wall condition. The initial data are inside a suitable class of functions of Sobolev type. We prove that the solutions of isentropic equations with ill-prepared initial data converge to the solution of the incompressible magnetohydrodynamic system by using the dispersion of acoustic waves in the half space. The incompressible limit of nonisentropic equations is rigorously established for well-prepared initial data.