A Strichartz inequality for the Schroedinger equation on non-trapping asymptotically conic manifolds
| dc.creator | Hassell, Andrew | |
| dc.creator | Tao, Terence | |
| dc.creator | Wunsch, Jared | |
| dc.date | 2003-12-11 | |
| dc.date | 2004-06-30 | |
| dc.date.accessioned | 2026-07-07T05:03:47Z | |
| dc.date.available | 2026-07-07T05:03:47Z | |
| dc.description | We obtain an $L^4$ space-time Strichartz inequality for any smooth three-dimensional Riemannian manifold $(M,g)$ which is asymptotically conic at infinity and non-trapping, where $u$ is a solution to the Schrödinger equation $iu_t + {1/2} Δ_M u = 0$. The exponent $H^{1/4}(M)$ is sharp, by scaling considerations. In particular our result covers asymptotically flat non-trapping manifolds. Our argument is based on the interaction Morawetz inequality introduced by Colliander et al., interpreted here as a positive commutator inequality for the tensor product $U(t,z',z'') := u(t,z') u(t,z'')$ of the solution with itself. We also use smoothing estimates for Schrödinger solutions including a new one proved here with weight $r^{-1}$ at infinity and with the gradient term involving only one angular derivative. | |
| dc.description | 43 pages, 1 figure; minor corrections to earlier version | |
| dc.identifier | https://arxiv.org/abs/math/0312225 | |
| dc.identifier | http://arxiv.org/abs/math/0312225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69557 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55, 58J40, 81Q05 | |
| dc.title | A Strichartz inequality for the Schroedinger equation on non-trapping asymptotically conic manifolds | |
| dc.type | text |