Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation

Shuji Machihara, Kenji Nakanishi, Tohru Ozawa

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1. The method of proof is based on the Strichartz estimate of Lt 2 type for Dirac and Klein-Gordon equations. We also prove that the solutions of the nonlinear Dirac equation after modulation of phase converge to the corresponding solutions of the nonlinear Schrödinger equation as the speed of light tends to infinity.

Original languageEnglish
Pages (from-to)179-194
Number of pages16
JournalRevista Matematica Iberoamericana
Volume19
Issue number1
Publication statusPublished - 2003
Externally publishedYes

Fingerprint

Non-relativistic Limit
Dirac Equation
Global Solution
Nonlinear Equations
Strichartz Estimates
Klein-Gordon Equation
Sobolev Spaces
Paul Adrien Maurice Dirac
Cauchy Problem
Modulation
Existence and Uniqueness
Infinity
Tend
Converge

Keywords

  • Nonlinear Dirac equation
  • Nonlinear Schrödinger equation
  • Nonrelativistic limit
  • Strichartz's estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation. / Machihara, Shuji; Nakanishi, Kenji; Ozawa, Tohru.

In: Revista Matematica Iberoamericana, Vol. 19, No. 1, 2003, p. 179-194.

Research output: Contribution to journalArticle

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