Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation
Machihara, Shuji ; Nakanishi, Kenji ; Ozawa, Tohru
Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, p. 179-194 / Harvested from Project Euclid
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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.
Publié le : 2003-03-15
Classification:  Nonlinear Dirac equation,  Strichartz's estimate,  nonrelativistic limit,  nonlinear Schrödinger equation,  35L70 
@article{1049123084,
     author = {Machihara, Shuji and Nakanishi, Kenji and Ozawa, Tohru},
     title = {Small global solutions and the nonrelativistic limit for
 the nonlinear Dirac equation},
     journal = {Rev. Mat. Iberoamericana},
     volume = {19},
     number = {2},
     year = {2003},
     pages = { 179-194},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049123084}
}

Machihara, Shuji; Nakanishi, Kenji; Ozawa, Tohru. Small global solutions and the nonrelativistic limit for
 the nonlinear Dirac equation. Rev. Mat. Iberoamericana, Tome 19 (2003) no. 2, pp.  179-194. http://gdmltest.u-ga.fr/item/1049123084/