Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
| dc.creator | Colliander, Jim | |
| dc.creator | Keel, Mark | |
| dc.creator | Staffilani, Gigliola | |
| dc.creator | Takaoka, Hideo | |
| dc.creator | Tao, Terence | |
| dc.date | 2002-06-20 | |
| dc.date | 2002-11-12 | |
| dc.date.accessioned | 2026-07-07T04:49:16Z | |
| dc.date.available | 2026-07-07T04:49:16Z | |
| dc.description | We study the long-time behaviour of the focusing cubic NLS on $\R$ in the Sobolev norms $H^s$ for $0 < s < 1$. We obtain polynomial growth-type upper bounds on the $H^s$ norms, and also limit any orbital $H^s$ instability of the ground state to polynomial growth at worst; this is a partial analogue of the $H^1$ orbital stability result of Weinstein. In the sequel to this paper we generalize this result to other nonlinear Schrödinger equations. Our arguments are based on the ``$I$-method'' from our earlier papers, which pushes down from the energy norm, as well as an ``upside-down $I$-method'' which pushes up from the $L^2$ norm. | |
| dc.description | updated draft | |
| dc.identifier | https://arxiv.org/abs/math/0206218 | |
| dc.identifier | http://arxiv.org/abs/math/0206218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64356 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55 | |
| dc.title | Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm | |
| dc.type | text |