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2009 Periodic stochastic Korteweg–de Vries equation with additive space-time white noise
Tadahiro Oh
Anal. PDE 2(3): 281-304 (2009). DOI: 10.2140/apde.2009.2.281

Abstract

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.

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Tadahiro Oh. "Periodic stochastic Korteweg–de Vries equation with additive space-time white noise." Anal. PDE 2 (3) 281 - 304, 2009. https://doi.org/10.2140/apde.2009.2.281

Information

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

zbMATH: 1190.35202
MathSciNet: MR2603800
Digital Object Identifier: 10.2140/apde.2009.2.281

Subjects:
Primary: 35Q53 , 60H15

Keywords: local well-posedness , stochastic KdV , White noise

Rights: Copyright © 2009 Mathematical Sciences Publishers

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