Global rough solutions for the Zakharov system in two spatial dimensions
Analysis of PDEs
2012-05-22 v2
Abstract
We show an improved global well-posedness result for the Zakharov system in two space dimensions with minimal regularity assumptions for the data. Especially we are able to allow Schroedinger and wave data, which do not belong to H^1 and L^2, respectively, thus with infinite energy. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao and bilinear estimates by Bejenaru, Herr, Holmer and Tataru. A polynomial growth bound for the solution is also given.
Cite
@article{arxiv.1203.2173,
title = {Global rough solutions for the Zakharov system in two spatial dimensions},
author = {Hartmut Pecher},
journal= {arXiv preprint arXiv:1203.2173},
year = {2012}
}
Comments
The paper is withdrawn because slightly better results were meanwhile given in arXiv:1203.6376v1