Scattering Below Critical Energy for the Radial 4D Yang-Mills Equation and for the 2D Corotational Wave Map System

Given g and f = gg', we consider solutions to the following non linear wave equation : [GRAPHICS] Under suitable assumptions on g, this equation admits non-constant stationary solutions : we denote Q one with least energy. We characterize completely the behavior as time goes to +/-infinity of solutions (u, u(t)) corresponding to data with energy less than or equal to the energy of Q : either it is (Q, 0) up to scaling, or it scatters in the energy space. Our results include the cases of the 2 dimensional corotational wave map system, with target S-2, in the critical energy space, as well as the 4 dimensional, radially symmetric Yang-Mills fields on Minkowski space, in the critical energy space.