On the well-posedness of the generalized korteweg-de vries equation in scale-critical Lr-space

Satoshi Masaki, Jun Ichi Segata

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The purpose of this paper is to study local and global well-posedness of the initial value problem for the generalized Korteweg-de Vries (gKdV) equation in Lr = (f ε S' (ℝ): ||f||Lr = ||f||Lr' ≤ ∞). We show (large-data) local well-posedness, small-data global well-posedness, and small-data scattering for the gKdV equation in the scale-critical Lr-space. A key ingredient is a Stein-Tomas-type inequality for the Airy equation, which generalizes the usual Strichartz estimates for Lr-framework.

Original languageEnglish
Pages (from-to)699-725
Number of pages27
JournalAnalysis and PDE
Volume9
Issue number3
DOIs
Publication statusPublished - 2016 Jan 1

Keywords

  • Generalized korteweg-de vries equation
  • Scattering problem

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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