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

Tadahiro Oh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the local well-posedness of the periodic stochastic Koreweg-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 Besove-type space (b) over cap (s)(p,infinity)(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 (s)(p,infinity)(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.

Original languageEnglish
Pages (from-to)281-304
Number of pages24
JournalAnalysis and PDE
Volume2
Issue number3
DOIs
Publication statusPublished - 2009

Keywords

  • stochastic KdV
  • local well-posedness
  • ILL-POSEDNESS
  • white noise
  • KDV

Fingerprint

Dive into the research topics of 'Periodic stochastic Korteweg–de Vries equation with additive space-time white noise'. Together they form a unique fingerprint.

Cite this