Global regularity of wave maps I. Small critical Sobolev norm in high dimension
| dc.creator | Tao, Terence | |
| dc.date | 2000-10-07 | |
| dc.date | 2000-12-02 | |
| dc.date.accessioned | 2026-07-07T04:37:53Z | |
| dc.date.available | 2026-07-07T04:37:53Z | |
| dc.description | We show that wave maps from Minkowski space $R^{1+n}$ to a sphere are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space $\dot H^{n/2}$ in the high dimensional case $n \geq 5$. A major difficulty, not present in the earlier results, is that the $\dot H^{n/2}$ norm barely fails to control $L^\infty$, potentially causing a logarithmic divergence in the nonlinearity; however, this can be overcome by using co-ordinate frames adapted to the wave map by approximate parallel transport. In the sequel of this paper we address the more interesting two-dimensional case, which is energy-critical. | |
| dc.description | 24 pages, no figures, to appear, IMRN. The continuity argument has been once again simplified, some references added, and more typoes have been eradicated | |
| dc.identifier | https://arxiv.org/abs/math/0010068 | |
| dc.identifier | http://arxiv.org/abs/math/0010068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60072 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J10 | |
| dc.title | Global regularity of wave maps I. Small critical Sobolev norm in high dimension | |
| dc.type | text |