  We study the initial-boundary value problem for 1D compressible MHD equations
of viscous non-resistive fluids in the Lagrangian mass coordinates. Based on
the estimates of upper and lower bounds of the density, weak solutions are
constructed by approximation of global regular solutions, the existence of
which has recently been obtained by Jiang and Zhang in [17]. Uniqueness of weak
solutions is also proved as a consequence of Lipschitz continuous dependence on
the initial data. Furthermore, long time behavior for global solutions is
investigated. Specifically, based on the uniform-in-time bounds of the density
from above and below away from zero, together with the structure of the
equations, we show the exponential decay rate in L^2- and H^1-norm
respectively, with initial data of arbitrarily large.
