Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

Shuji Machihara; Kenji Nakanishi; Tohru Ozawa

doi:10.1007/s002080200008

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

Shuji Machihara^*, Kenji Nakanishi, Tohru Ozawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

90 Citations (Scopus)

Abstract

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schrödinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in L².

Original language	English
Pages (from-to)	603-621
Number of pages	19
Journal	Mathematische Annalen
Volume	322
Issue number	3
DOIs	https://doi.org/10.1007/s002080200008
Publication status	Published - 2002 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s002080200008

Cite this

@article{b5f76d28646d40daa680cb51d4147f3b,

title = "Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations",

abstract = "We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr{\"o}dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in L2.",

author = "Shuji Machihara and Kenji Nakanishi and Tohru Ozawa",

year = "2002",

month = dec,

day = "1",

doi = "10.1007/s002080200008",

language = "English",

volume = "322",

pages = "603--621",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

AU - Machihara, Shuji

AU - Nakanishi, Kenji

AU - Ozawa, Tohru

PY - 2002/12/1

Y1 - 2002/12/1

N2 - We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schrödinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in L2.

AB - We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schrödinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in L2.

UR - http://www.scopus.com/inward/record.url?scp=0036013587&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036013587&partnerID=8YFLogxK

U2 - 10.1007/s002080200008

DO - 10.1007/s002080200008

M3 - Article

AN - SCOPUS:0036013587

SN - 0025-5831

VL - 322

SP - 603

EP - 621

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this