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This paper is concerned with the asymptotic behaviors of global strongsolutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD)equations with large initial perturbations in two-dimensional periodic domainsin Lagrangian coordinates. First, motivated by the odevity conditions imposedin [Arch. Ration. Mech. Anal. 227 (2018), 637--662], we prove the existence anduniqueness 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 magneticfield. Then, we establish time-decay rates of strong solutions. Moreover, wefind that $H^2$-norm of the velocity decays faster than the perturbed magneticfield. Finally, by developing some new analysis techniques, we show that thestrong solution convergence in a rate of the field strength to the solution ofthe corresponding linearized problem as the strength of the impressive magneticfield goes to infinity. In addition, an extension of similar results to thecorresponding inviscid case with damping is presented.

Asymptotic Behaviors of Global Solutions to the Two-Dimensional Non-resistive MHD Equations with Large Initial Perturbations