Periodic solutions of the korteweg-de vries equation driven by white noise

A. De Bouard; A. Debussche; Y. Tsutsumi

doi:10.1137/S0036141003425301

Periodic solutions of the korteweg-de vries equation driven by white noise

A. De Bouard, A. Debussche, Y. Tsutsumi

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

Abstract

We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time, and "almost white in space." We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the method which was introduced by Bourgain, but based here on Besov spaces.

Original language	English
Pages (from-to)	815-855
Number of pages	41
Journal	SIAM Journal on Mathematical Analysis
Volume	36
Issue number	3
DOIs	https://doi.org/10.1137/S0036141003425301
Publication status	Published - 27 May 2005
Externally published	Yes

Keywords

Besov spaces
Korteweg-de Vries equation
Stochastic partial differential equations
White noise

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10.1137/S0036141003425301

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title = "Periodic solutions of the korteweg-de vries equation driven by white noise",

abstract = "We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time, and {"}almost white in space.{"} We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the method which was introduced by Bourgain, but based here on Besov spaces.",

keywords = "Besov spaces, Korteweg-de Vries equation, Stochastic partial differential equations, White noise",

author = "\{De Bouard\}, A. and A. Debussche and Y. Tsutsumi",

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AU - De Bouard, A.

AU - Debussche, A.

AU - Tsutsumi, Y.

PY - 2005/5/27

Y1 - 2005/5/27

N2 - We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time, and "almost white in space." We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the method which was introduced by Bourgain, but based here on Besov spaces.

AB - We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time, and "almost white in space." We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the method which was introduced by Bourgain, but based here on Besov spaces.

KW - Besov spaces

KW - Korteweg-de Vries equation

KW - Stochastic partial differential equations

KW - White noise

U2 - 10.1137/S0036141003425301

DO - 10.1137/S0036141003425301

M3 - Article

AN - SCOPUS:18744372434

SN - 0036-1410

VL - 36

SP - 815

EP - 855

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

Periodic solutions of the korteweg-de vries equation driven by white noise

Abstract

Keywords

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