Global existence and uniqueness of Schrödinger maps in dimensions d... 4

Abstract In dimensions d ⩾ 4 , we prove that the Schrodinger map initial-value problem { ∂ t s = s × Δ s on R d × R ; s ( 0 ) = s 0 admits a unique solution s : R d × R → S 2 ↪ R 3 , s ∈ C ( R : H Q ∞ ) , provided that s 0 ∈ H Q ∞ and ‖ s 0 − Q ‖ H ˙ d / 2 ≪ 1 , where Q ∈ S 2 .

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