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

Terence Tao

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arXiv · 0908.0776

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

Terence Tao

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Abstract

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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Terence Tao. 2009-08-08. Global regularity of wave maps VII. Control of delocalised or dispersed solutions. https://arxiv.org/abs/0908.0776

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