An inverse theorem for the bilinear $L^2$ Strichartz estimate for the wave equation
| dc.creator | Tao, Terence | |
| dc.date | 2009-04-19 | |
| dc.date.accessioned | 2026-07-07T13:05:50Z | |
| dc.date.available | 2026-07-07T13:05:50Z | |
| dc.description | A standard bilinear $L^2$ Strichartz estimate for the wave equation, which underlies the theory of $X^{s,b}$ spaces of Bourgain and Klainerman-Machedon, asserts (roughly speaking) that if two finite-energy solutions to the wave equation are supported in transverse regions of the light cone in frequency space, then their product lies in spacetime $L^2$ with a quantitative bound. In this paper we consider the \emph{inverse problem} for this estimate: if the product of two waves has large $L^2$ norm, what does this tell us about the waves themselves? The main result, roughly speaking, is that the lower-frequency wave is dispersed away from a bounded number of light rays. This result will be used in a forthcoming paper \cite{tao:heatwave4} of the author on the global regularity problem for wave maps. | |
| dc.description | 20 pages, no figures. To be submitted in conjunction with other "heatwave" papers | |
| dc.identifier | https://arxiv.org/abs/0904.2880 | |
| dc.identifier | http://arxiv.org/abs/0904.2880 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227617 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L05 | |
| dc.title | An inverse theorem for the bilinear $L^2$ Strichartz estimate for the wave equation | |
| dc.type | text |