  We study a generalization of energy super-critical wave maps due to Adkins
and Nappi that can also be viewed as a simplified version of the Skyrme model.
These are maps from 1+3 dimensional Minkowski space that take values in the
3-sphere, and it follows that every finite energy Adkins-Nappi wave map has a
fixed topological degree which is an integer. Here we initiate the study of the
large data dynamics for Adkins-Nappi wave maps by proving that there is no type
II blow-up in the class of maps with topological degree zero. In particular,
any degree zero map whose critical norm stays bounded must be global-in-time
and scatter to zero as time tends to infinity.
