Periodic solutions of the Korteweg-de Vries equation driven by white noise

被引：21

作者：

De Bouard, A

Debussche, A

Tsutsumi, Y

机构：

[1] CNRS, F-91405 Orsay, France

[2] Univ Paris 11, UMR 8628, F-91405 Orsay, France

[3] ENS Cachan, F-35170 Bruz, France

[4] Tohoku Univ, Inst Math, Sendai, Miyagi 9808578, Japan

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2004年 / 36卷 / 03期

关键词：

Korteweg-de Vries equation; stochastic partial differential equations; white noise; Besov spaces;

D O I：

10.1137/S0036141003425301

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：815 / 855

页数：41

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