  In this paper, we establish the continuous dependence for the non-resistive
MHD equations in Sobolev spaces. Our obtained result fills considerably the
recent result [C. Fefferman, D. McCormick, J. Robinson and J. Rodrigo, Higher
order commutator estimates and local existence for the non-resistive MHD
equations and related models, J. Funct. Anal. 267 (2014), 1035--1056] for the
continuous dependence on initial data. We also show that this result is
optimal. More precisely, we proved that the data-to-solution map is not uniform
continuous dependence in Sobolev spaces.
