  The paper is concerned with the free boundary problem for 2D current-vortex
sheets in ideal incompressible magneto-hydrodynamics near the transition point
between the linearized stability and instability. In order to study the
dynamics of the discontinuity near the onset of the instability, Hunter and
Thoo have introduced an asymptotic quadratically nonlinear integro-differential
equation for the amplitude of small perturbations of the planar discontinuity.
The local-in-time existence of smooth solutions to the Cauchy problem for the
amplitude equation was already shown. In the present paper we prove the
continuous dependence in strong norm of solutions on the initial data. This
completes the proof of the well-posedness of the problem in the classical sense
of Hadamard.
