Stable soliton resolution for the corotational Skyrme model

Abstract

We study the classical Skyrme model. Under corotational symmetry, we prove that (i) stationary solutions, or Skyrmions, are unique in every topological degree; (ii) the Cauchy problem is globally well-posed in a nonlinear energy space; and (iii) stable soliton resolution holds: every finite-energy solution scatters to the Skyrmion of the same degree. Our key observation is that subcritical equivariant Yang–Mills dynamics emerge near the origin and suppress concentration.