  We consider the decay problem for global solutions of the Skyrme and
Adkins-Nappi equations. We prove that the energy associated to any bounded
energy solution of the Skyrme (or Adkins-Nappi) equation decays to zero outside
the light cone (in the radial coordinate). Furthermore, we prove that suitable
polynomial weighted energies of any small solution decays to zero when these
energies are bounded. The proof consists of finding three new virial type
estimates, one for the exterior of the light cone, based on the energy of the
solution, and a more subtle virial identity for the weighted energies, based on
a modification of momentum type quantities.
