Vol. 2, No. 3, 2009

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

Tadahiro Oh

Vol. 2 (2009), No. 3, 281–304
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 = 1 2+, 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.

Keywords
stochastic KdV, white noise, local well-posedness
Mathematical Subject Classification 2000
Primary: 35Q53, 60H15
Milestones
Received: 2 January 2009
Revised: 28 August 2009
Accepted: 19 October 2009
Published: 9 February 2010
Authors
Tadahiro Oh
Department of Mathematics
University of Toronto
40 St. George Street, Rm 6290
Toronto, ON  M5S 2E4
Canada