TY - JOUR
T1 - Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation
AU - Machihara, Shuji
AU - Nakanishi, Kenji
AU - Ozawa, Tohru
PY - 2003
Y1 - 2003
N2 - 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 Lt2 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.
AB - 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 Lt2 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.
KW - Nonlinear Dirac equation
KW - Nonlinear Schrödinger equation
KW - Nonrelativistic limit
KW - Strichartz's estimate
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U2 - 10.4171/RMI/342
DO - 10.4171/RMI/342
M3 - Article
AN - SCOPUS:0037570590
SN - 0213-2230
VL - 19
SP - 179
EP - 194
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
IS - 1
ER -