Global regularity of wave maps VII. Control of delocalised or dispersed solutions
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.
Keywords
Cite
@article{arxiv.0908.0776,
title = {Global regularity of wave maps VII. Control of delocalised or dispersed solutions},
author = {Terence Tao},
journal= {arXiv preprint arXiv:0908.0776},
year = {2009}
}
Comments
125 pages, one figure. Some references added. Will not be published in current form, pending future reorganisation of the heatwave project