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In the present paper, we prove the a priori estimates of Sobolev norms for afree boundary problem of the incompressible inviscid MHD equations in allphysical spatial dimensions $n=2$ and 3 by adopting a geometrical point of viewused in Christodoulou-Lindblad CPAM 2000, and estimating quantities such as thesecond fundamental form and the velocity of the free surface. We identify thewell-posedness condition that the outer normal derivative of the total pressureincluding the fluid and magnetic pressures is negative on the free boundary,which is similar to the physical condition (Taylor sign condition) for theincompressible Euler equations of fluids.

A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows