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This paper is concerned with existence of solutions to the incompressiblenon-resistive viscous magnetohydrodynamic (MHD) equations with large initialperturbations in there-dimensional (3D) periodic domains (in Lagrangiancoordinates). Motivated by the Diophantine condition imposed by the approximatetheory of non-resistive MHD equations in \cite{BCSCSPLL}, Chen--Zhang--Zhou in\cite{chen2021} and the magnetic inhibition mechanism of Lagrangian coordinatesversion in our previous paper \cite{JFJSOMITIN}, we prove the existence ofunique classical solutions under some class of large initial perturbations,where the intensity of impressive magnetic fields depends increasingly on the $H^{17}\times H^{21}$-norm of the initial perturbation of both the velocity andmagnetic field. Our result not only mathematically verifies that magneticfields prevent the singularity formation of solutions with large initialvelocity in the viscous case, but also provide a starting point for theexistence theory of large perturbation solutions of the 3D non-resistiveviscous MHD equations. In addition, we further rigorously prove that, for largetime or strong magnetic field, the MHD equations reduce to the correspondinglinearized equations by providing the error estimates, which enjoy the types ofalgebraic decay with respect to the both of time and field intensity, betweenthe solutions of both the nonlinear and linear equations.

On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids: Existence of Solutions in Some Classes of Large Data