Analysis & PDE
- Anal. PDE
- Volume 2, Number 3 (2009), 281-304.
Periodic stochastic Korteweg–de Vries equation with additive space-time white noise
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 for , such that . In establishing local well-posedness, we use a variant of the Bourgain space adapted to 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 , the space of finite Borel measures on .
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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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. https://projecteuclid.org/euclid.apde/1513798038