A priori estimates for 3D incompressible current-vortex sheets (Q411369)

This article deals with the equations governing the motion of a perfectly conducting inviscid incompressible homogeneous plasma. The free boundary problem for current-vortex sheets is considered. This problem is reduced to a fixed domain by considering a suitable change of variables. The control of the function describing the free interface follows from a stability condition. An a priori estimate for smooth solutions in Sobolev norm is obtained by showing the boundedness of a higher-order energy functional.