WELL-POSEDNESS AND SCATTERING FOR A SYSTEM OF QUADRATIC DERIVATIVE NONLINEAR SCHRODINGER EQUATIONS WITH LOW REGULARITY INITIAL DATA

In the present paper, we consider the Cauchy problem of a system of quadratic derivative nonlinear Schrodinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. The local existence of the solution of the system in the Sobolev space H-s for s > d/2 + 3 is proved by M. Colin and T. Colin. We prove the well-posedness of the system with low regularity initial data. For some cases, we also prove the well-posedness and the scattering at the scaling critical regularity by using U-2 space and V-2 space which are applied to prove the well-posedness and the scattering for KP-II equation at the scaling critical regularity by Hadac, Herr and Koch (2009).