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Strichartz estimates on Kerr black hole backgrounds


Author: Mihai Tohaneanu
Journal: Trans. Amer. Math. Soc. 364 (2012), 689-702
MSC (2010): Primary 35Q75
DOI: https://doi.org/10.1090/S0002-9947-2011-05405-X
Published electronically: September 29, 2011
MathSciNet review: 2846348
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Abstract: We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. This follows a local energy decay result for the Kerr space-time obtained in earlier work of Tataru and the author, and uses the techniques and results by the author and collaborators (2010). As an application, we then prove global well-posedness and uniqueness for the energy critical semilinear wave equation with small initial data.


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Additional Information

Mihai Tohaneanu
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Address at time of publication: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218

DOI: https://doi.org/10.1090/S0002-9947-2011-05405-X
Received by editor(s): January 8, 2010
Published electronically: September 29, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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