Stochastic Korteweg-de Vries equation driven by fractional Brownian motion

Guolian  Wang; Boling Guo

doi:10.3934/dcds.2015.35.5255

Article Contents

2015, Volume 35, Issue 11: 5255-5272. Doi: 10.3934/dcds.2015.35.5255

This issue Previous Article Exponential convergence of non-linear monotone SPDEs Next Article On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: The critical case

Stochastic Korteweg-de Vries equation driven by fractional Brownian motion

Guolian Wang^1, and
Boling Guo^2,

1.
Department of Mathematics, Tongji University, Shanghai 200092
2.
Institute of Applied Physics & Computational Math., Beijing 100088

Received: August 31, 2013

Revised: April 30, 2014

Published: October 2015

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Abstract

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 $H\geq\frac{7}{16}$ of the fBm, we obtain the local existence results with initial value in classical Sobolev spaces $H^s$ with $s\geq -\frac{9}{16}$. 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.

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Mathematics Subject Classification: Primary: 35R60, 35Q53; Secondary: 60H15.

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