Scattering for the non-radial 3D cubic nonlinear Schroedinger equation
| dc.creator | Duyckaerts, Thomas | |
| dc.creator | Holmer, Justin | |
| dc.creator | Roudenko, Svetlana | |
| dc.date | 2007-10-19 | |
| dc.date | 2007-12-04 | |
| dc.date.accessioned | 2026-07-07T08:46:39Z | |
| dc.date.available | 2026-07-07T08:46:39Z | |
| dc.description | Scattering of radial $H^1$ solutions to the 3D focusing cubic nonlinear Schrödinger equation below a mass-energy threshold $M[u]E[u] < M[Q]E[Q]$ and satisfying an initial mass-gradient bound $\|u_0\|_{L^2} \|\nabla u_0 \|_{L^2} < \|Q\|_{L^2} \|\nabla Q\|_{L^2}$, where $Q$ is the ground state, was established in Holmer-Roudenko (2007). In this note, we extend the result in Holmer-Roudenko (2007) to non-radial $H^1$ data. For this, we prove a non-radial profile decomposition involving a spatial translation parameter. Then, in the spirit of Kenig-Merle (2006), we control via momentum conservation the rate of divergence of the spatial translation parameter and by a convexity argument based on a local virial identity deduce scattering. An application to the defocusing case is also mentioned. | |
| dc.identifier | https://arxiv.org/abs/0710.3630 | |
| dc.identifier | http://arxiv.org/abs/0710.3630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143320 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Scattering for the non-radial 3D cubic nonlinear Schroedinger equation | |
| dc.type | text |