On global existence and scattering for the wave maps equation

Abstract

We prove global existence and scattering for the wave-maps equation in n + 1 dimensions, n = 2, 3, for initial data which is small in the scale-invariant homogeneous Besov space Ḃ 2,1 n /2 x Ḃ 2,1 n /2-1 . This result was proved in an earlier paper by the author for n ≥ 4.