= Small data global regularity for wave maps
Smooth compatible data sufficiently small in high weighted <Sobolev norms> relative to a constant map produce global smooth <wave maps> in three and four spatial dimensions. In four dimensions, derivative decay $(1+t)^{-3/2}$ is time-integrable and closes <commuted wave energy> estimates. In three dimensions the weaker $(1+t)^{-1}$ decay requires the cancellation of <null forms for wave equations>, exploited by the <vector field method for wave equations>. These classical localized-data statements do not assert global regularity from small supercritical energy alone.
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