We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables u : ℝd x x ℝt → C and n : ℝd x × ℝt → ℝ. The Zakharov system is known to be locally well-posed in (u, n) ε L 2, ×H-1/2 and the Klein-Gordon- Schrödinger system is known to be locally well-posed in (u, n) ε L2× L2. Here, we show that the Zakharov and Klein-Gordon-Schrödinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the L2 norm of u and controlling the growth of n via the estimates in the local theory.
- Global wellposedness
- Klein-gordon-schödinger system
- Zakharov system
ASJC Scopus subject areas
- Applied Mathematics