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Pointwise decay for semilinear wave equations on Kerr spacetimes

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Abstract

In this article, we prove pointwise bounds for solutions to the semilinear wave equation with integer powers \(p\ge 3\) on Kerr backgrounds with small angular momentum and small initial data. We expect that the bounds proved in this paper are optimal.

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Notes

  1. In Kerr one can actually control a stronger norm, where the r-derivative does not degenerate at the trapped set. However, we do not need the stronger norm in this paper.

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Acknowledgements

The author would like to thank Sung-Jin Oh, Shi-Zhuo Looi and Hans Lindblad for many useful conversations regarding the paper, and the Korea Institute for Advanced Study for their hospitality during the spring of 2019. The author was partly supported by the Simons collaboration Grant 586051.

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  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Mihai Tohaneanu

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Correspondence to Mihai Tohaneanu.

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Tohaneanu, M. Pointwise decay for semilinear wave equations on Kerr spacetimes. Lett Math Phys 112, 6 (2022). https://doi.org/10.1007/s11005-021-01495-x

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  • DOI: https://doi.org/10.1007/s11005-021-01495-x

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