On the Stochastic Korteweg-de Vries Equation

A. De Bouard; A. Debussche

doi:10.1006/jfan.1997.3184

On the Stochastic Korteweg-de Vries Equation

A. De Bouard, A. Debussche

Centre national de la recherche scientifique

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a stochastic Korteweg-de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions inH¹(R) in the case of additive noise and existence of martingales solutions inL²(R) in the case of multiplicative noise.

Original language	English
Pages (from-to)	215-251
Number of pages	37
Journal	Journal of Functional Analysis
Volume	154
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1997.3184
Publication status	Published - 1 Apr 1998

Keywords

Korteweg-de Vries equation; stochastic partial differential equations; non-linear random water waves

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10.1006/jfan.1997.3184

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title = "On the Stochastic Korteweg-de Vries Equation",

abstract = "We consider a stochastic Korteweg-de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions inH1(R) in the case of additive noise and existence of martingales solutions inL2(R) in the case of multiplicative noise.",

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AU - De Bouard, A.

AU - Debussche, A.

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N2 - We consider a stochastic Korteweg-de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions inH1(R) in the case of additive noise and existence of martingales solutions inL2(R) in the case of multiplicative noise.

AB - We consider a stochastic Korteweg-de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions inH1(R) in the case of additive noise and existence of martingales solutions inL2(R) in the case of multiplicative noise.

KW - Korteweg-de Vries equation; stochastic partial differential equations; non-linear random water waves

U2 - 10.1006/jfan.1997.3184

DO - 10.1006/jfan.1997.3184

M3 - Article

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SN - 0022-1236

VL - 154

SP - 215

EP - 251

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

On the Stochastic Korteweg-de Vries Equation

Abstract

Keywords

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