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We describe the asymptotic behavior as time goes to infinity of solutions ofthe 2 dimensional corotational wave map system and of solutions to the 4dimensional, radially symmetric Yang-Mills equation, in the critical energyspace, with data of energy smaller than or equal to a harmonic map of minimalenergy. An alternative holds: either the data is the harmonic map and thesoltuion is constant in time, or the solution scatters in infinite time.

Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system