  It is shown that the Cauchy problem of the equations in magnetohydrodynamics
in the whole space is globally well-posed for any initial smooth and localized
data. In general, the mathematical structure of solution shows that the coupled
magnetic-vortical field has the characters of turbulence, if the initial data
exceed certain size. In particular, if a strong magnetic force dominates the
flow evolution, the current density possesses a cubic non-linearity. The
solution of the non-linear problem has been constructed and has been expressed
as an infinite series.
