Invariance of the Gibbs measure for the Schrödinger-Benjamin-Ono system

Tadahiro Oh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We prove the invariance of the Gibbs measure for the periodic Schrodinger-Benjamin-Ono system (when the coupling parameter vertical bar gamma vertical bar not equal 0, 1) by establishing a new local well-posedness in a modified Sobolev space and constructing the Gibbs measure ( which is in the sub-L(2) setting for the Benjamin Ono part). We also show the ill-posedness result in H(s)(T) x H(s-1/2)(T) for s <1/2 when vertical bar gamma vertical bar not equal 0, 1 and for any s is an element of R when vertical bar gamma vertical bar = 1.

Original languageEnglish
Pages (from-to)2207-2225
Number of pages19
JournalSIAM Journal on Mathematical Analysis
Volume41
Issue number6
DOIs
Publication statusPublished - 2009

Keywords / Materials (for Non-textual outputs)

  • Schrodinger
  • Benjamin-Ono
  • Gibbs measures
  • a.s. global well-posedness
  • ill-posedness

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