On the decay of solutions to a class of defocusing NLS
| dc.creator | Visciglia, Nicola | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:41Z | |
| dc.date.available | 2026-07-07T10:17:41Z | |
| dc.description | We consider the following family of Cauchy problems: {equation*} i\partial_t u= Δu - u|u|^α, (t,x) \in \R \times \R^d {equation*} $$u(0)=φ\in H^1(\R^d)$$ where $0<α<\frac 4{d-2}$ for $d\geq 3$ and $0<α<\infty$ for $d=1,2$. We prove that the $L^r$-norms of the solutions decay as $t\to \pm \infty$, provided that $2<r<\frac{2d}{d-2}$ when $d\geq 3$ and $2<r<\infty$ when $d=1,2$. In particular we extend previous results obtained by Ginibre and Velo for $d\geq 3$ and by Nakanishi for $d=1,2$, where the same decay results are proved under the extra assumption $α>\frac 4d$. | |
| dc.description | 8 | |
| dc.identifier | https://arxiv.org/abs/0811.1849 | |
| dc.identifier | http://arxiv.org/abs/0811.1849 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173938 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35B40 ; 35Q55 | |
| dc.title | On the decay of solutions to a class of defocusing NLS | |
| dc.type | text |