Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with low regularity periodic initial data

Abstract

We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved the small data global well-posedness and the scattering at the scaling critical regularity for $d\ge 2$ when the coefficients of Laplacian satisfy some condition. In the present paper, we prove the well-posedness of the system for the periodic case. In particular, well-posedness is proved at the scaling critical regularity for $d\ge 3$ under some condition for the coefficients of Laplacian.

This paper is withdrawn, as it is now incorporated into arXiv:2407.03565