%0 Journal Article
%T Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schr£żdinger systems
%A Jim Colliander
%A Justin Holmer
%A Nikolaos Tzirakis
%J Mathematics
%D 2006
%I arXiv
%X We prove low-regularity global well-posedness for the 1d Zakharov system and 3d Klein-Gordon-Schr\"odinger system, which are systems in two variables $u:\mathbb{R}_x^d\times \mathbb{R}_t \to \mathbb{C}$ and $n:\mathbb{R}^d_x\times \mathbb{R}_t\to \mathbb{R}$. The Zakharov system is known to be locally well-posed in $(u,n)\in L^2\times H^{-1/2}$ and the Klein-Gordon-Schr\"odinger system is known to be locally well-posed in $(u,n)\in L^2\times L^2$. Here, we show that the Zakharov and Klein-Gordon-Schr\"odinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the $L^2$ norm of $u$ and controlling the growth of $n$ via the estimates in the local theory.
%U http://arxiv.org/abs/math/0603595v1