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

Raphaël Côte (1) , Carlos Kenig (2) , Frank Merle (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Department of Mathematics [Chicago]
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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

Mots clés: Wave map; Yang-mills; scattering; energy critical

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Raphaël Côte, Carlos Kenig, Frank Merle. Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Communications in Mathematical Physics, 2008, 284 (1), pp.203-225. ⟨10.1007/s00220-008-0604-4⟩. ⟨hal-00221387⟩