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The Strauss conjecture on Kerr black hole backgrounds

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Abstract

We examine solutions to semilinear wave equations on black hole backgrounds and give a proof of an analog of the Strauss conjecture on the Schwarzschild and Kerr, with small angular momentum, black hole backgrounds. The key estimates are a class of weighted Strichartz estimates, which are used near infinity where the metrics can be viewed as small perturbations of the Minkowski metric, and a localized energy estimate on the black hole background, which handles the behavior in the remaining compact set.

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Acknowledgments

The first three authors were supported in part by the NSF. The fifth author was supported by Zhejiang Provincial Natural Science Foundation of China LR12A01002, the Fundamental Research Funds for the Central Universities, NSFC 11301478, 11271322 and J1210038.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Hans Lindblad, Christopher D. Sogge & Mihai Tohaneanu

  2. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599-3250, USA

    Jason Metcalfe

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Chengbo Wang

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  1. Hans Lindblad
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  2. Jason Metcalfe
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  3. Christopher D. Sogge
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  4. Mihai Tohaneanu
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  5. Chengbo Wang
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Correspondence to Chengbo Wang.

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Lindblad, H., Metcalfe, J., Sogge, C.D. et al. The Strauss conjecture on Kerr black hole backgrounds. Math. Ann. 359, 637–661 (2014). https://doi.org/10.1007/s00208-014-1006-x

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  • DOI: https://doi.org/10.1007/s00208-014-1006-x

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