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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Strichartz estimates on Kerr black hole backgrounds
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by Mihai Tohaneanu PDF
Trans. Amer. Math. Soc. 364 (2012), 689-702 Request permission

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
  • Received by editor(s): January 8, 2010
  • Published electronically: September 29, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 689-702
  • MSC (2010): Primary 35Q75
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05405-X
  • MathSciNet review: 2846348