Intermediate long wave equation in negative Sobolev spaces

Andreia Chapouto, Justin Forlano, Guopeng Li, Tadahiro Oh, Didier Pilod

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity s = −1/2 as the critical regularity for ILW with any depth parameter, by establishing the following two results. (i) By viewing ILW as a perturbation of the Benjamin–Ono equation (BO) and exploiting the complete integrability of BO, we establish a global-in-time a priori bound on the Hs-norm of a solution to ILW for −1/2 <s<0. (ii) By making use of explicit 2 solutions, we prove that ILW is ill-posed in Hs for s<−1/2. Our results apply to both the real line case and the periodic case.

Original languageEnglish
Pages (from-to)452-468
Number of pages17
JournalProceedings of the American Mathematical Society, Series B
Volume11
Issue number1
DOIs
Publication statusPublished - 12 Sept 2024
Externally publishedYes

Keywords

  • a priori bound
  • Benjamin–Ono equation
  • complete integrability
  • ill-posedness
  • Intermediate long wave equation

Cite this