Semilinear Schrödinger Flows on Hyperbolic Spaces: Scattering in H^1
| dc.creator | Ionescu, Alexandru D. | |
| dc.creator | Staffilani, Gigliola | |
| dc.date | 2008-01-18 | |
| dc.date.accessioned | 2026-07-07T08:55:23Z | |
| dc.date.available | 2026-07-07T08:55:23Z | |
| dc.description | We prove global well-posedness and scattering in $H^1$ for the defocusing nonlinear Schrödinger equations \begin{equation*} \begin{cases} &(i\partial_t+Δ_\g)u=u|u|^{2σ}; &u(0)=ϕ, \end{cases} \end{equation*} on the hyperbolic spaces $\H^d$, $d\geq 2$, for exponents $σ\in(0,2/(d-2))$. The main unexpected conclusion is scattering to linear solutions in the case of small exponents $σ$; for comparison, on Euclidean spaces scattering in $H^1$ is not known for any exponent $σ\in(1/d,2/d]$ and is known to fail for $σ\in(0,1/d]$. Our main ingredients are certain noneuclidean global in time Strichartz estimates and noneuclidean Morawetz inequalities. | |
| dc.identifier | https://arxiv.org/abs/0801.2957 | |
| dc.identifier | http://arxiv.org/abs/0801.2957 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146256 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Semilinear Schrödinger Flows on Hyperbolic Spaces: Scattering in H^1 | |
| dc.type | text |