On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation
| dc.creator | Tao, Terence | |
| dc.date | 2003-09-26 | |
| dc.date | 2004-03-13 | |
| dc.date.accessioned | 2026-07-07T05:01:28Z | |
| dc.date.available | 2026-07-07T05:01:28Z | |
| dc.description | We study the asymptotic behavior of large data radial solutions to the focusing Schrödinger equation $i u_t + Δu = -|u|^2 u$ in $\R^3$, assuming globally bounded $H^1(\R^3)$ norm (i.e. no blowup in the energy space). We show that as $t \to \pm \infty$, these solutions split into the sum of three terms: a radiation term that evolves according to the linear Schrödinger equation, a smooth function localized near the origin, and an error that goes to zero in the $\dot H^1(\R^3)$ norm. Furthermore, the smooth function near the origin is either zero (in which case one has scattering to a free solution), or has mass and energy bounded strictly away from zero, and obeys an asymptotic Pohozaev identity. These results are consistent with the conjecture of soliton resolution. | |
| dc.description | 51 pages, no figures, to appear, Journal of Partial Differential Equations and Dynamical Systems. Some minor corrections and typos fixed from previous version | |
| dc.identifier | https://arxiv.org/abs/math/0309428 | |
| dc.identifier | http://arxiv.org/abs/math/0309428 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68681 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55 | |
| dc.title | On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation | |
| dc.type | text |