  We consider 1-equivariant wave maps from 1+2 dimensions to the 2-sphere of
finite energy. We establish a classification of all degree 1 global solutions
whose energies are less than three times the energy of the harmonic map Q. In
particular, for each global energy solution of topological degree 1, we show
that the solution asymptotically decouples into a rescaled harmonic map plus a
radiation term. Together with our companion article, where we consider the case
of finite-time blow up, this gives a characterization of all 1-equivariant,
degree 1 wave maps in the energy regime [E(Q), 3E(Q)).

Analysis of PDEs