Invariance of the White Noise for KdV

Tadahiro Oh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space (b) over cap (s)(p, infinity), sp <-1, contains the support of the white noise. Then, we prove local well-posedness in (s)(p, infinity) for p = 2+, s = -1/2+ such that sp <-1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko [21].

Original languageEnglish
Pages (from-to)217-236
Number of pages20
JournalCommunications in Mathematical Physics
Volume292
Issue number1
DOIs
Publication statusPublished - Nov 2009

Keywords / Materials (for Non-textual outputs)

  • CAUCHY-PROBLEM
  • ILL-POSEDNESS
  • ZAKHAROV SYSTEM
  • NONLINEAR SCHRODINGER-EQUATION
  • WELL-POSEDNESS

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