Normal form and global solutions for the Klein-Gordon-Zakharov equations

Tohru Ozawa, K. Tsutaya, Y. Tsutsumi

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper we study the global existence and asymptotic behavior of solutions for the Cauchy problem of the Klein-Gordon-Zakharov equations in three space dimensions. We prove that for small initial data, there exist the unique global solutions of the Klein-Gordon-Zakharov equations. We also show that these solutions approach asymptotically the free solutions as t → ∞. Our proof is based on the method of normal forms introduced by Shatah [12], which transforms the original system with quadratic nonlinearity into a new system with cubic nonlinearity.

Original languageEnglish
Pages (from-to)459-503
Number of pages45
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume12
Issue number4
DOIs
Publication statusPublished - 2016 Jul 1
Externally publishedYes

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Klein-Gordon Equation
Global Solution
Normal Form
Nonlinearity
Asymptotic Behavior of Solutions
Global Existence
Cauchy Problem
Transform

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

Cite this

Normal form and global solutions for the Klein-Gordon-Zakharov equations. / Ozawa, Tohru; Tsutaya, K.; Tsutsumi, Y.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 12, No. 4, 01.07.2016, p. 459-503.

Research output: Contribution to journalArticle

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