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.
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Daniel Tataru (2001) studied this question.
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