Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations |
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| Authors: | Shuji Machihara Kenji Nakanishi Tohru Ozawa |
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| Affiliation: | (1) Department of Mathematics, Hokkaido University, Sapporo, 060-0810 Japan , JP;(2) Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan , JP |
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| 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?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002 |
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