Geometric renormalization of large energy wave maps
| dc.creator | Tao, Terence | |
| dc.date | 2004-11-16 | |
| dc.date.accessioned | 2026-07-07T05:14:22Z | |
| dc.date.available | 2026-07-07T05:14:22Z | |
| dc.description | There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy of the solution is large. In this report we present a different renormalization, based on the harmonic map heat flow, which works for large energy wave maps from two dimensions to hyperbolic spaces. We also observe an intriguing estimate of ``non-concentration'' type, which asserts roughly speaking that if the energy of a wave map concentrates at a point, then it becomes asymptotically self-similar. | |
| dc.description | 28 pages, no figures, submitted, Forges les Eaux conference proceedings | |
| dc.identifier | https://arxiv.org/abs/math/0411354 | |
| dc.identifier | http://arxiv.org/abs/math/0411354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73253 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J10 | |
| dc.title | Geometric renormalization of large energy wave maps | |
| dc.type | text |