Random data Cauchy problem for supercritical Schrödinger equations
| dc.creator | Thomann, Laurent | |
| dc.date | 2009-01-27 | |
| dc.date.accessioned | 2026-07-07T12:35:30Z | |
| dc.date.available | 2026-07-07T12:35:30Z | |
| dc.description | In this paper we consider the Schrödinger equation with power-like nonlinearity and confining potential or without potential. This equation is known to be well-posed with data in a Sobolev space $\H^{s}$ if $s$ is large enough and strongly ill-posed is $s$ is below some critical threshold $s_{c}$. Here we use the randomisation method of the inital conditions, introduced by N. Burq-N. Tzvetkov and we are able to show that the equation admits strong solutions for data in $\H^{s}$ for some $s<s_{c}$. In the appendix we prove the equivalence between the smoothing effect for a Schrödinger operator with confining potential and the decay of the associate spectral projectors. | |
| dc.description | 29 pages, 0 figure | |
| dc.identifier | https://arxiv.org/abs/0901.4238 | |
| dc.identifier | http://arxiv.org/abs/0901.4238 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217785 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35A07; 35B35; 35B05; 37L50; 35Q55 | |
| dc.title | Random data Cauchy problem for supercritical Schrödinger equations | |
| dc.type | text |