  In this article, we consider the evolutionary model for magnetoelasticity
with vanishing viscosity/damping, which is a nonlinear dispersive system. The
global regularity and scattering of the evolutionary model for
magnetoelasticity under small size of initial data is proved. Our proof relies
on the idea of vector-field method due to the quasilinearity and the presence
of convective term. A key observation is that we construct a suitable energy
functional including the mass quantity, which enable us to provide a good decay
estimates for Schr\"odinger flow. In particular, we establish the asymptotic
behavior in both mass and energy spaces for Schr\"odinger map, not only for
gauged equation.
