Quasi-invariant Gaussian measures for the cubic nonlinear Schrödinger equation with third order dispersion

Tadahiro Oh, Yoshio Tsutsumi, Nikolay Tzvetkov

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the cubic nonlinear Schrödinger equation with third order dispersion on the circle. In the non-resonant case, we prove that the mean-zero Gaussian measures on Sobolev spaces H^s(핋), s>3/4, are quasi-invariant under the flow. In establishing the result, we apply gauge transformations to remove the resonant part of the dynamics and use invariance of the Gaussian measures under these gauge transformations.
Original languageEnglish
Pages (from-to)366-381
Number of pages16
JournalComptes Rendus Mathématique
Volume357
Issue number4
DOIs
Publication statusPublished - 23 Apr 2019

Keywords

  • third order nonlinear Schrödinger equation
  • Gaussian measure
  • quasi-invariance
  • non-resonance

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