GLOBAL WELL-POSEDNESS FOR HALF-WAVE MAPS WITH S2 AND H2 TARGETS FOR SMALL SMOOTH INITIAL DATA

We prove global well-posedness for the half-wave map with S-2 target for small H-n/2 x Hn/2-1 initial data. We also prove the global well-posedness for the equation with H-2 target for small smooth B-2,1(n/2) x B-2,1(n/2-1) initial data.

Automated summary

Global well-posedness for the half-wave map with S-2 target for small initial data and equation with H-2 target for small initial data has been proven. This result is significant for the understanding and study of the behavior of these equations with given initial conditions.