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

Abstract

<p style='text-indent:20px;'>This paper consider the Cauchy problem for the Schr<inline-formula><tex-math id="M1">\begin{document}$ {\rm \ddot{o}} $\end{document}</tex-math></inline-formula>dinger equation coupled with the stochastic Benjamin-Ono equation. A priori estimates for the stochastic integral and the nonlinear terms corresponding to the coupling system are achieved by using Fourier transform restriction method introduced by Bourgain. It is shown that the Cauchy problem is locally well-posed as the initial data in appropriate Sobolev spaces.</p>