Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation

Tadahiro Oh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We consider Cauchy problems of some dispersive PDEs with random initial data. In particular, we construct local-in-time solutions to the mean-zero periodic KdV almost surely for the initial data in the support of the mean-zero Gaussian measures on H(s)(T), s > s(0) where s(0) = -11/6 + root 61/6 approximate to -0.5316 <-1/2, by exhibiting nonlinear smoothing under randomization on the second iteration of the Duhamel formulation. We also show that there is no nonlinear smoothing for the dispersionless cubic Szego equation under randomization of initial data.

Original languageEnglish
Pages (from-to)335-365
Number of pages31
JournalFunkcialaj ekvacioj-Serio internacia
Volume54
Issue number3
Publication statusPublished - Dec 2011

Keywords / Materials (for Non-textual outputs)

  • well-posedness
  • nonlinear smoothing
  • KdV
  • Szegö equation

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