An improved local well-posedness result for the one-dimensional Zakharov system
| dc.creator | Pecher, Hartmut | |
| dc.date | 2006-11-27 | |
| dc.date | 2008-01-23 | |
| dc.date.accessioned | 2026-07-07T08:55:53Z | |
| dc.date.available | 2026-07-07T08:55:53Z | |
| dc.description | The 1D Cauchy problem for the Zakharov system is shown to be locally well-posed for low regularity Schrödinger data u_0 \in \hat{H^{k,p}} and wave data (n_0,n_1) \in \hat{H^{l,p}} \times \hat{H^{l-1,p}} under certain assumptions on the parameters k,l and 1<p\le 2, where \|u_0\|_{\hat{H^{k,p}}} := \| < ξ>^k \hat{u_0}\|_{L^{p'}}, generalizing the results for p=2 by Ginibre, Tsutsumi, and Velo. Especially we are able to improve the results from the scaling point of view, and also allow suitable k<0, l<-1/2, i.e. data u_0 \not\in L^2 and (n_0,n_1)\not\in H^{-1/2}\times H^{-3/2}, which was excluded in the case p=2. | |
| dc.description | 17 pages. Final version to appear in Journal of Mathematical Analysis and Applications | |
| dc.identifier | https://arxiv.org/abs/math/0611811 | |
| dc.identifier | http://arxiv.org/abs/math/0611811 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146423 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55; 35L70 | |
| dc.title | An improved local well-posedness result for the one-dimensional Zakharov system | |
| dc.type | text |