Well-posedness of stochastic KdV-BO equation driven by fractional Brownian motion

作者：Bian Baojun; Wang Guolian^*

来源：Applied Mathematics and Computation, 2014, 243: 657-669.

DOI：10.1016/j.amc.2014.05.114

• Korteweg-de Vries Benjamin-Ono equation
• Fourier restriction norm
• Fractional Brownian motion
• Hurst parameter

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 B-H. 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 B-H. With H > 3/8, we prove local existence results with initial value in classical Sobolev spaces of negative indices, i.e. H-s with s >= -1/8.

• 出版日期2014-9-15
• 单位同济大学