The Strauss conjecture on Kerr black hole backgrounds

Hans Lindblad; Jason Metcalfe; Christopher D. Sogge; Mihai Tohaneanu; Chengbo Wang

doi:10.1007/s00208-014-1006-x

The Strauss conjecture on Kerr black hole backgrounds

Hans Lindblad
, Jason Metcalfe
, Christopher D. Sogge
, Mihai Tohaneanu
, Chengbo Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

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.

Original language	English
Pages (from-to)	637-661
Number of pages	25
Journal	Mathematische Annalen
Volume	359
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-014-1006-x
State	Published - Aug 2014

Bibliographical note

Funding Information:
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.

Funding

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.

Funders	Funder number
National Natural Science Foundation of China (NSFC)
National Science Foundation Arctic Social Science Program
National Science Foundation Arctic Social Science Program	1054289
National Natural Science Foundation of China (NSFC)	J1210038, 11271322, 11301478
Natural Science Foundation of Zhejiang Province	LR12A01002
Fundamental Research Funds for the Central Universities

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-014-1006-x

Cite this

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title = "The Strauss conjecture on Kerr black hole backgrounds",

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.",

author = "Hans Lindblad and Jason Metcalfe and Sogge, \{Christopher D.\} and Mihai Tohaneanu and Chengbo Wang",

note = "Funding Information: 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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AU - Sogge, Christopher D.

AU - Tohaneanu, Mihai

AU - Wang, Chengbo

N1 - Funding Information: 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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N2 - 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.

AB - 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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JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

The Strauss conjecture on Kerr black hole backgrounds

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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