Analysis & PDE

  • Anal. PDE
  • Volume 2, Number 3 (2009), 281-304.

Periodic stochastic Korteweg–de Vries equation with additive space-time white noise

Tadahiro Oh

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We prove the local well-posedness of the periodic stochastic Korteweg–de Vries equation with the additive space-time white noise. To treat low regularity of the white noise in space, we consider the Cauchy problem in the Besov-type space b̂p,s(T) for s=12+, p=2+ such that sp<1. In establishing local well-posedness, we use a variant of the Bourgain space adapted to b̂p,s(T) and establish a nonlinear estimate on the second iteration on the integral formulation. The deterministic part of the nonlinear estimate also yields the local well-posedness of the deterministic KdV in M(T), the space of finite Borel measures on T.

Article information

Anal. PDE, Volume 2, Number 3 (2009), 281-304.

Received: 2 January 2009
Revised: 28 August 2009
Accepted: 19 October 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 60H15: Stochastic partial differential equations [See also 35R60]

stochastic KdV white noise local well-posedness


Oh, Tadahiro. Periodic stochastic Korteweg–de Vries equation with additive space-time white noise. Anal. PDE 2 (2009), no. 3, 281--304. doi:10.2140/apde.2009.2.281.

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