  We prove the local well-posedness of the 3D free-boundary incompressible
ideal magnetohydrodynamics (MHD) equations with surface tension, which describe
the motion of a perfect conducting fluid in an electromagnetic field. We adapt
the ideas developed in the remarkable paper [11] by Coutand and Shkoller to
generate an approximate problem with artificial viscosity indexed by $\kappa>0$
whose solution converges to that of the MHD equations as $\kappa\to 0$.
However, the local well-posedness of the MHD equations is no easy consequence
of Euler equations thanks to the strong coupling between the velocity and
magnetic fields. This paper is the continuation of the second and third
authors' previous work [38] in which the a priori energy estimate for
incompressible free-boundary MHD with surface tension is established. But the
existence is not a trivial consequence of the a priori estimate as it cannot be
adapted directly to the approximate problem due to the loss of the symmetric
structure.
