Local ill-posedness of the 1D Zakharov system
| dc.creator | Holmer, Justin | |
| dc.date | 2006-02-08 | |
| dc.date | 2006-08-24 | |
| dc.date.accessioned | 2026-07-07T07:03:13Z | |
| dc.date.available | 2026-07-07T07:03:13Z | |
| dc.description | Ginibre-Tsutsumi-Velo (1997) proved local well-posedness for the Zakharov system for any dimension $d$, in the inhomogeneous Sobolev spaces $(u,n)\in H^k(\mathbb{R}^d)\times H^s(\mathbb{R}^d)$ for a range of exponents $k$, $s$ depending on $d$. Here we restrict to dimension $d=1$ and present a few results establishing local ill-posedness for exponent pairs $(k,s)$ outside of the well-posedness regime. The techniques employed are rooted in the work of Bourgain (1993), Birnir-Kenig-Ponce-Svanstedt-Vega (1996), and Christ-Colliander-Tao (2003) applied to the nonlinear Schroedinger equation. | |
| dc.identifier | https://arxiv.org/abs/math/0602153 | |
| dc.identifier | http://arxiv.org/abs/math/0602153 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108891 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55 | |
| dc.title | Local ill-posedness of the 1D Zakharov system | |
| dc.type | text |