Global regularity of wave maps VII. Control of delocalised or dispersed solutions

Details Global regularity of wave maps VII. Control of delocalised or dispersed solutions Global regularity of wave maps VII. Control of delocalised or dispersed solutions

2009-08-06

arxiv.org/abs/0908.0776v2

Mathematics

Analysis of PDEs

125 pages, one figure. Some references added. Will not be published in current form, pending future reorganisation of the heat

Scientific paper

This is the final paper in the series \cite{tao:heatwave}, \cite{tao:heatwave2}, \cite{tao:heatwave3}, \cite{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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