Global Well-Posedness for the $L^2$-critical nonlinear Schrödinger equation in higher dimensions
| dc.creator | De Silva, Daniela | |
| dc.creator | Pavlovic, Natasa | |
| dc.creator | Staffilani, Gigliola | |
| dc.creator | Tzirakis, Nikolaos | |
| dc.date | 2006-07-25 | |
| dc.date.accessioned | 2026-07-07T07:20:54Z | |
| dc.date.available | 2026-07-07T07:20:54Z | |
| dc.description | The initial value problem for the $L^{2}$ critical semilinear Schrödinger equation in $\R^n, n \geq 3$ is considered. We show that the problem is globally well posed in $H^{s}({\Bbb R^{n}})$ when $1>s>\frac{\sqrt{7}-1}{3}$ for $n=3$, and when $1>s> \frac{-(n-2)+\sqrt{(n-2)^2+8(n-2)}}{4}$ for $n \geq 4$. We use the ``$I$-method'' combined with a local in time Morawetz estimate. | |
| dc.description | 18 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0607632 | |
| dc.identifier | http://arxiv.org/abs/math/0607632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115117 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Global Well-Posedness for the $L^2$-critical nonlinear Schrödinger equation in higher dimensions | |
| dc.type | text |