Invariant Gibbs measures and a.s. global well-posedness for coupled KdV systems

Tadahiro Oh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We continue our study of the well-posedness theory of a one-parameter family of coupled KdV-type systems in the periodic setting. When the value of a coupling parameter alpha is an element of (0,4)\{1}, we show that the Gibbs measure is invariant under the flow and the system is globally well posed almost surely on the statistical ensemble, provided that certain Diophantine conditions are satisfied.

Original languageEnglish
Pages (from-to)637-668
Number of pages32
JournalDifferential and integral equations
Volume22
Issue number7-8
Publication statusPublished - 2009

Keywords

  • KdV
  • well-posedness
  • Gibbs measure
  • Diophantine condition

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