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Global existence for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator in low dimensions

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Abstract

We show that the small solution for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator exists globally in dimension 1 and 2. Moreover, we prove that the Sobolev norm of the solution grows at most polynomially.

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Authors and Affiliations

  1. School of Mathematics, East China University of Science and Technology, Meilong Road 130, Shanghai, 200237, China

    Lingyun Xue & Qidi Zhang

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  1. Lingyun Xue
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  2. Qidi Zhang
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Correspondence to Qidi Zhang.

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This work was supported by National Natural Science Foundation of China Grant No. 11601154.

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Xue, L., Zhang, Q. Global existence for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator in low dimensions. Nonlinear Differ. Equ. Appl. 29, 50 (2022). https://doi.org/10.1007/s00030-022-00776-1

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  • DOI: https://doi.org/10.1007/s00030-022-00776-1

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