JournalsrmiVol. 19, No. 1pp. 179–194

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

  • Shuji Machihara

    Shimane University, Matsue, Japan
  • Kenji Nakanishi

    Kyoto University, Japan
  • Tohru Ozawa

    Hokkaido University, Sapporo, Japan
Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation cover

Abstract

In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space HsH^s. We prove the existence and uniqueness of global solutions for small data in HsH^s with s>1s>1. The method of proof is based on the Strichartz estimate of Lt2L^2_t 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 Schröodinger equation as the speed of light tends to infinity.

Cite this article

Shuji Machihara, Kenji Nakanishi, Tohru Ozawa, Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation. Rev. Mat. Iberoam. 19 (2003), no. 1, pp. 179–194

DOI 10.4171/RMI/342