Instability of the periodic nonlinear Schrodinger equation
| dc.creator | Christ, Michael | |
| dc.creator | Colliander, James | |
| dc.creator | Tao, Terence | |
| dc.date | 2003-11-13 | |
| dc.date.accessioned | 2026-07-07T05:02:53Z | |
| dc.date.available | 2026-07-07T05:02:53Z | |
| dc.description | We study the periodic non-linear Schrodinger equations with odd integer power nonlinearities, for initial data which are assumed to be small in some negative order Sobolev space, but which may have large L^2 mass. These equations are known to be illposed in H^s for all negative s, in the sense that the solution map fails to be uniformly continuous from H^s to itself, even for short times and small norms. Here we show that these equations are even more unstable. For the cubic equation, the solution map is discontinuous from H^s to even the space of distributions. For the quintic and higher order nonlinearities, there exist pairs of solutions which are uniformly bounded in H^s, are arbitrarily close in any C^N norm at time zero, and fail to be close in the distribution topology at an arbitrarily small positive time. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311227 | |
| dc.identifier | http://arxiv.org/abs/math/0311227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69185 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55, 35L70 | |
| dc.title | Instability of the periodic nonlinear Schrodinger equation | |
| dc.type | text |