Global solutions of the Klein–Gordon–Schrödinger system with rough data in

In this paper, we consider the Klein–Gordon–Schrödinger system with quadratic (Yakuwa) coupling and cubic autointeractions in , and prove the existence and uniqueness of global solution for rough data. The techniques to be used are adapted from a general scheme originally introduced by J. Bourgain to split the data into the low and high frequency parts.