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 journalArticlepeer-review

90 Citations (Scopus)


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 languageEnglish
Pages (from-to)603-621
Number of pages19
JournalMathematische Annalen
Issue number3
Publication statusPublished - 2002 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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