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March, 2003 Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation
Shuji Machihara, Kenji Nakanishi, Tohru Ozawa
Rev. Mat. Iberoamericana 19(1): 179-194 (March, 2003).

Abstract

In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space $H^s$. We prove the existence and uniqueness of global solutions for small data in $H^s$ with $s>1$. The method of proof is based on the Strichartz estimate of $L^2_t$ 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.

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Shuji Machihara. Kenji Nakanishi. Tohru Ozawa. "Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation." Rev. Mat. Iberoamericana 19 (1) 179 - 194, March, 2003.

Information

Published: March, 2003
First available in Project Euclid: 31 March 2003

zbMATH: 1041.35061
MathSciNet: MR1993419

Subjects:
Primary: 35L70

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.19 • No. 1 • March, 2003
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