The cauchy problem for the Klein-Gordon-Schrödinger system in low dimensions below the energy space

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Abstract

We show that the Klein-Gordon-Schrödinger system in one, two, and three dimensions has a global solution below the energy space. The proof uses the I-method recently introduced by Colliander et al. (2001) and mixed type Strichartz estimates for the solutions of Schrödinger and Klein-Gordon equations, respectively.

Original languageEnglish (US)
Pages (from-to)605-641
Number of pages37
JournalCommunications in Partial Differential Equations
Volume30
Issue number4-6
DOIs
StatePublished - Aug 18 2005
Externally publishedYes

Keywords

  • Global well-posedness
  • Klein-Gordon-Schrödinger system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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