On the construction of solutions to the free-surface incompressible ideal magnetohydrodynamic equations

摘要

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. (C) 2019 Elsevier Masson SAS. All rights reserved.