White noise for KdV and mKdV on the circle

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We survey different approaches to study the invariance of the white noise for the periodic KdV. We mainly discuss the following two methods. First, we discuss the PDE method, following Bourgain [2], in a general framework. Then, we show how it can be applied to the low regularity setting of the white noise for KdV by introducing the Besov-type space \hat{b}^s_{p, \infty}, sp < −1. Secondly, we describe the probabilistic method by Quastel, Valk\'o, and the author [41]. We also use this probabilistic approach to study the white noise for mKdV.
Original languageEnglish
Pages (from-to)99-124
Number of pages26
JournalRIMS Kôkyûroku Bessatsu
VolumeB18
Publication statusPublished - 2010

Keywords / Materials (for Non-textual outputs)

  • Kdv
  • mKdV
  • cubic NLS
  • white noise
  • invariant measure

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