  This paper is concerned with the asymptotic behaviors of global strong
solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD)
equations with large initial perturbations in two-dimensional periodic domains
in Lagrangian coordinates. First, motivated by the odevity conditions imposed
in [Arch. Ration. Mech. Anal. 227 (2018), 637--662], we prove the existence and
uniqueness of strong solutions under some class of large initial perturbations,
where the strength of impressive magnetic fields depends increasingly on the
$H^2$-norm of the initial perturbation values of both velocity and magnetic
field. Then, we establish time-decay rates of strong solutions. Moreover, we
find that $H^2$-norm of the velocity decays faster than the perturbed magnetic
field. Finally, by developing some new analysis techniques, we show that the
strong solution convergence in a rate of the field strength to the solution of
the corresponding linearized problem as the strength of the impressive magnetic
field goes to infinity. In addition, an extension of similar results to the
corresponding inviscid case with damping is presented.
