In this paper, we consider the stochastic Burgers' equation driven by a genuine cylindrical fractional Brownian motion with Hurst parameter H > 1 4 . We first prove the regularities of the solution to the linear stochastic problem corresponding to the stochastic Burgers' equation. Then we obtain the local and global existence and uniqueness results for the stochastic Burgers' equation.

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In this paper, we consider the stochastic Korteweg-de VriesBenjamin-Ono equation with white noise. Using Fourier restriction norm method and some basic inequalities, we obtain a local existence and uniqueness result for the solution of this problem. We also get global existence of the L 2 (R) solution.

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<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>