  We construct and study global solutions for the 3-dimensional incompressible
MHD systems with arbitrary small viscosity. In particular, we provide a
rigorous justification for the following dynamical phenomenon observed in many
contexts: the solution initially behaves like non-dispersive waves and the
shape of the solution persists for a very long time (proportional to the
Reynolds number), thereafter, the solution will be damped due to the long-time
accumulation of the diffusive effects, eventually, the total energy of the
system becomes extremely small compared to the viscosity so that the diffusion
takes over and the solution afterwards decays fast in time.
  We do not assume any condition on the symmetry or on the vorticity. The size
of data and the a priori estimates do not depend on viscosity. The proof is
builded upon a novel use of the basic energy identity and a geometric study of
the characteristic hypersurfaces. The approach is partly inspired by
Christodoulou-Klainerman's proof of the nonlinear stability of Minkowski space
in general relativity.
