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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.
Anthony Christopher Davison, Sophie Myriam Hautphenne