Global regularity of wave maps VII. Control of delocalised or dispersed solutions
Abstract
This is the final paper in the series tao:heatwave, tao:heatwave2, tao:heatwave3, tao:heatwave4 that establishes global regularity for two-dimensional wave maps into hyperbolic targets. In this paper we establish the remaining claims required for this statement, namely a divisible perturbation theory, and a means of synthesising solutions for frequency-delocalised, spatially-dispersed, or spatially-delocalised data out of solutions of strictly smaller energy. As a consequence of the perturbation theory here and the results obtained earlier in the series, we also establish spacetime bounds and scattering properties of wave maps into hyperbolic space.
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