Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance |
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Authors: | Yuichiro Kawahara |
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Institution: | a Doshisha Junior and Senior High School, Iwakura, Sakyo-ku, Kyoto 606-8558, Japan b Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan |
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Abstract: | We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses m1, m2 satisfying the resonance relation m2=2m1>0. We introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at the rate O(|t|−1) as t→±∞ in L∞. In particular, our new condition includes the Yukawa type interaction, which has been excluded from the null condition in the sense of J.-M. Delort, D. Fang and R. Xue J.-M. Delort, D. Fang, R. Xue, Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions, J. Funct. Anal. 211 (2004) 288-323]. |
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Keywords: | 35L70 35B40 35L15 |
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