On the construction of solutions to the free-surface incompressible   ideal magnetohydrodynamic equations
  We consider a free boundary problem for the incompressible ideal magnetohydrodynamic equations that describes the motion of the plasma in vacuum. The magnetic field is tangent and the total pressure vanishes along the plasma-vacuum interface. Under the Taylor sign condition of the total pressure on the free surface, we prove the local well-posedness of the problem in Sobolev spaces. 
Xumin Gu and Yanjin Wang
math.AP