Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrodinger systems

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrodinger system, which are systems in two variables u : R-x(d) x R-t --> C and n : R-x(d) x R-t --> R. The Zakharov system is known to be locally well-posed in (u, n) is an element of L-2 x H-1/2 and the Klein-Gordon-Schrodinger system is known to be locally well-posed in (u, n) is an element of L-2 x L-2. Here, we show that the Zakharov and Klein- Gordon-Schrodinger 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.