STOCHASTIC KORTEWEG-DE VRIES EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

被引：2

作者：

Wang, Guolian ^{[1
]}

Guo, Boling ^{[2
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Korteweg-de Vries equation; fractional Brownian motion; Hurst parameter; stochastic convolution; bilinear estimate; EVOLUTION-EQUATIONS; NOISE; SOLITONS;

D O I：

10.3934/dcds.2015.35.5255

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for the Korteweg-de Vries equation driven by a cylindrical fractional Brownian motion (fBm) in this paper. With Hurst parameter H >= 7/16 of the fBm, we obtain the local existence results with initial value in classical Sobolev spaces H-s with s >= -9/16. Furthermore, we give the relation between the Hurst parameter H and the index s to the Sobolev spaces H-s, which finds out the regularity between the driven term fBm and the initial value for the stochastic Korteweg-de Vries equation.

引用

页码：5255 / 5272

页数：18

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