A Stochastic Weakly Damped, Forced KdV-BO Equation

Wang, Guolian

doi:10.1155/2014/576087

Abstract and Applied Analysis

2014

DOI: 10.1155/2014/576087

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A Stochastic Weakly Damped, Forced KdV-BO Equation

Guolian Wang

Abstract: We investigate the long time behavior of the damped, forced KdV-BO equation driven by white noise. We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the spaceH1(ℝ).

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2023

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Cited by 1 publication

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The local well-posedness for a stochastic system of nonlinear dispersive equations

Wang¹,

Zhang²

2023

DCDS-B

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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>

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The local well-posedness for a stochastic system of nonlinear dispersive equations

Wang¹,

Zhang²

2023

DCDS-B

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A Stochastic Weakly Damped, Forced KdV-BO Equation

Cited by 1 publication

References 12 publications

The local well-posedness for a stochastic system of nonlinear dispersive equations

The local well-posedness for a stochastic system of nonlinear dispersive equations

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