Abstract
The Cauchy problem for the Korteweg–de Vries Benjamin–Ono equation driven by cylindrical fractional Brownian motion is discussed in this paper. Fractional Brownian motion is a family of processes BH. It is known that the smaller the value of Hurst parameter H is, the worse of the regularity of fBm is. Using Bourgain restriction method, we obtain the lower bound of the Hurst parameter H for the driving processes BH. With H>38, we prove local existence results with initial value in classical Sobolev spaces of negative indices, i.e. Hs with s⩾-18.
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