Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case
| dc.creator | Miao, Changxing | |
| dc.creator | Xu, Guixiang | |
| dc.creator | Zhao, Lifeng | |
| dc.date | 2008-07-04 | |
| dc.date | 2008-11-13 | |
| dc.date.accessioned | 2026-07-07T13:00:29Z | |
| dc.date.available | 2026-07-07T13:00:29Z | |
| dc.description | We consider the focusing energy-critical nonlinear Schrödinger equation of fourth order $iu_t+Δ^2 u=|u|^\frac{8}{d-4}u$. We prove that if a maximal-lifespan radial solution $u: I\times\Bbb R^d\to\mathbb{C}$ obeys $\displaystyle\sup_{t\in I}\|Δu(t)\|_{2}<\|ΔW\|_{2}$, then it is global and scatters both forward and backward in time. Here $W$ denotes the ground state, which is a stationary solution of the equation. In particular, if a solution has both energy and kinetic energy less than those of the ground state $W$ at some point in time, then the solution is global and scatters. | |
| dc.description | 37 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/0807.0690 | |
| dc.identifier | http://arxiv.org/abs/0807.0690 | |
| dc.identifier | J. Differential Equations 246 (2009) 3715-3749 | |
| dc.identifier | doi:10.1016/j.jde.2008.11.011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225856 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q40, 35Q55, 47J35. | |
| dc.title | Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case | |
| dc.type | text |