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 language | English |
|---|---|
| Pages (from-to) | 179-194 |
| Number of pages | 16 |
| Journal | Revista Matematica Iberoamericana |
| Volume | 19 |
| Issue number | 1 |
| Publication status | Published - 2003 |
| Externally published | Yes |
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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 journal › Article
}
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 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.
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 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.
KW - Nonlinear Dirac equation
KW - Nonlinear Schrödinger equation
KW - Nonrelativistic limit
KW - Strichartz's estimate
UR - http://www.scopus.com/inward/record.url?scp=0037570590&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037570590&partnerID=8YFLogxK
M3 - Article
VL - 19
SP - 179
EP - 194
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
SN - 0213-2230
IS - 1
ER -