The Alfven waves are fundamental wave phenomena in magnetized plasmas and the dynamics of Alfven waves are governed by the MHD system. In the talk, we construct and study the long time behavior of (viscous and non-viscous) Alfven waves.
As applications, (1) We provide a rigorous justification for the following dynamical phenomenon observed in many contexts: the solution at the beginning behave 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;
(2) We prove the rigidity aspects of the scattering problem for the MHD equations: We prove that the Alfven waves must vanish if their scattering fields vanish at infinities.