Minimal-mass blowup solutions of the mass-critical NLS
| dc.creator | Tao, Terence | |
| dc.creator | Visan, Monica | |
| dc.creator | Zhang, Xiaoyi | |
| dc.date | 2006-09-25 | |
| dc.date | 2006-10-16 | |
| dc.date.accessioned | 2026-07-07T07:25:13Z | |
| dc.date.available | 2026-07-07T07:25:13Z | |
| dc.description | We consider the minimal mass $m_0$ required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation $iu_t + Δu = μ|u|^{4/d} u$ to blow up. If $m_0$ is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in $L^2_x(\R^d)$ is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, \cite{keraani}, in dimensions 1, 2 and Begout and Vargas, \cite{begout}, in dimensions $d\geq 3$ for the mass-critical NLS and by Kenig and Merle, \cite{merlekenig}, in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in $L^2_x(\R^d)$ for the defocusing NLS in three and higher dimensions with spherically symmetric data. | |
| dc.description | Contains updated references and related remarks | |
| dc.identifier | https://arxiv.org/abs/math/0609690 | |
| dc.identifier | http://arxiv.org/abs/math/0609690 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116643 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Minimal-mass blowup solutions of the mass-critical NLS | |
| dc.type | text |