Mathematische Annalen

, Volume 322, Issue 3, pp 603–621

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

  • Shuji Machihara
  • Kenji Nakanishi
  • Tohru Ozawa
Original article

DOI: 10.1007/s002080200008

Cite this article as:
Machihara, S., Nakanishi, K. & Ozawa, T. Math Ann (2002) 322: 603. doi:10.1007/s002080200008

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 \(L^2\).

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Shuji Machihara
    • 1
  • Kenji Nakanishi
    • 2
  • Tohru Ozawa
    • 1
  1. 1.Department of Mathematics, Hokkaido University, Sapporo, 060-0810 Japan JP
  2. 2.Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan JP