Global dynamics for the stochastic KdV equation with white noise as initial data

Tadahiro Oh, Jeremy Quastel, Philippe Sosoe

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We study the stochastic Korteweg-de Vries equation (SKdV) with an additive space-time white noise forcing, posed on the one-dimensional torus. In particular, we construct global-in-time solutions to SKdV with spatial white noise initial data.
Due to the lack of an invariant measure, Bourgain's invariant measure argument is not applicable to this problem. In order to overcome this difficulty, we implement a variant of Bourgain's argument in the context of an evolution system of measures and construct global-in-time dynamics. Moreover, we show that the white noise measure with variance 1+t is an evolution system of measures for SKdV with the white noise initial data.
Original languageEnglish
Pages (from-to)420-460
Number of pages41
JournalTransactions of the American Mathematical Society
Publication statusPublished - 21 Feb 2024

Keywords / Materials (for Non-textual outputs)

  • Korteweg-de Vries equations
  • stochastic Korteweg-de Vries equations
  • white noise
  • evolution system of measures
  • invariant measure


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