The local well-posedness for a stochastic system of nonlinear dispersive equations

This paper consider the Cauchy problem for Schr$ {\rm \ddot{o}} $dinger equation coupled with stochastic Benjamin-Ono equation. A priori estimates integral and nonlinear terms corresponding to coupling system are achieved by using Fourier transform restriction method introduced Bourgain. It is shown that locally well-posed as initial data in appropriate Sobolev spaces.