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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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The Glassey conjecture on asymptotically flat manifolds
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by Chengbo Wang PDF
Trans. Amer. Math. Soc. 367 (2015), 7429-7451 Request permission

Abstract:

We verify the $3$-dimensional Glassey conjecture on asymptotically flat manifolds $(\mathbb {R}^{1+3},\mathfrak {g})$, where the metric $\mathfrak {g}$ is a certain small space-time perturbation of the flat metric, as well as the nontrapping asymptotically Euclidean manifolds. Moreover, for radial asymptotically flat manifolds $(\mathbb {R}^{1+n},\mathfrak {g})$ with $n\ge 3$, we verify the Glassey conjecture in the radial case. High dimensional wave equations with higher regularity are also discussed. The main idea is to exploit local energy and KSS estimates with variable coefficients, together with the weighted Sobolev estimates including trace estimates.
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Additional Information
  • Chengbo Wang
  • Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
  • MR Author ID: 766167
  • ORCID: 0000-0002-4878-7629
  • Email: wangcbo@gmail.com
  • Received by editor(s): June 28, 2013
  • Received by editor(s) in revised form: March 10, 2014
  • Published electronically: September 23, 2014
  • Additional Notes: The author was supported by the Zhejiang Provincial Natural Science Foundation of China LR12A01002, the Fundamental Research Funds for the Central Universities, NSFC 11301478, 11271322 and J1210038.
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 7429-7451
  • MSC (2010): Primary 35L70, 35L15
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06423-4
  • MathSciNet review: 3378835