Stability of energy-critical nonlinear Schrödinger equations in high dimensions
| dc.creator | Tao, Terence | |
| dc.creator | Visan, Monica | |
| dc.date | 2005-07-01 | |
| dc.date | 2005-07-09 | |
| dc.date.accessioned | 2026-07-07T05:21:17Z | |
| dc.date.available | 2026-07-07T05:21:17Z | |
| dc.description | We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions $n \geq 3$, for solutions which have large, but finite, energy and large, but finite, Strichartz norms. For dimensions $n \leq 6$, this theory is a standard extension of the small data well-posedness theory based on iteration in Strichartz spaces. However, in dimensions $n > 6$ there is an obstruction to this approach because of the subquadratic nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz). We resolve this by iterating in exotic Strichartz spaces instead. The theory developed here will be applied in a subsequent paper of the second author, to establish global well-posedness and scattering for the defocusing energy-critical equation for large energy data. | |
| dc.description | 30 pages, no figures, submitted, Electron. J. Diff. Eq. A new reference added | |
| dc.identifier | https://arxiv.org/abs/math/0507005 | |
| dc.identifier | http://arxiv.org/abs/math/0507005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75636 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L10 | |
| dc.title | Stability of energy-critical nonlinear Schrödinger equations in high dimensions | |
| dc.type | text |