Abstract
We prove a long time existence result for semi-linear Klein–Gordon equations with a superquadratic potential for small and smooth initial datum. The proof relies on a weak separation of eigenvalues and specific multilinear estimates of eigenfunctions of superquadratic oscillators.
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The author would like to thank Qidi Zhang and Jean-Marc Delort for valuable discussions.
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Communicated by D. Lannes.
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Imekraz, R. Normal form for semi-linear Klein–Gordon equations with superquadratic oscillators. Monatsh Math 179, 535–575 (2016). https://doi.org/10.1007/s00605-015-0739-2
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DOI: https://doi.org/10.1007/s00605-015-0739-2