Characterization of large energy solutions of the equivariant wave map problem: II

Raphaël Côte (1) , Carlos Kenig (2) , Andrew Lawrie (2) , Wilhelm Schlag (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Department of Mathematics

We consider 1-equivariant wave maps from 1+2 dimensions to the 2-sphere of finite energy. We establish a classification of all degree 1 global solutions whose energies are less than three times the energy of the harmonic map Q. In particular, for each global energy solution of topological degree 1, we show that the solution asymptotically decouples into a rescaled harmonic map plus a radiation term. Together with our companion article, where we consider the case of finite-time blow up, this gives a characterization of all 1-equivariant, degree 1 wave maps in the energy regime [E(Q), 3E(Q)).

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Côte, Carlos Kenig, Andrew Lawrie, Wilhelm Schlag. Characterization of large energy solutions of the equivariant wave map problem: II. American Journal of Mathematics, 2015, 137 (1), pp.209-250. ⟨10.1353/ajm.2015.0003⟩. ⟨hal-00832752⟩