L^2-concentration phenomenon for Zakharov system below energy norm
Analysis of PDEs
2007-05-23 v1
Abstract
In this paper, we'll prove a L^2-concentration result of Zakharov system in space dimension two, with radial initial data (u_0,n_0,n_1)\in H^s\times L^2\times H^{-1} ({16/17}<s<1), when blow up of the solution happens by I-method. In additional to that we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgain's to above spaces.
Cite
@article{arxiv.math/0702181,
title = {L^2-concentration phenomenon for Zakharov system below energy norm},
author = {Daoyuan Fang and Sijia Zhong},
journal= {arXiv preprint arXiv:math/0702181},
year = {2007}
}