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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 defocusing energy-supercritical nonlinear wave equation in three space dimensions
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by Rowan Killip and Monica Visan PDF
Trans. Amer. Math. Soc. 363 (2011), 3893-3934 Request permission

Abstract:

We consider the defocusing nonlinear wave equation $u_{tt}-\Delta u + |u|^p u=0$ in the energy-supercritical regime $p>4$. For even values of the power $p$, we show that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that solutions with bounded critical Sobolev norm are global and scatter. The impetus to consider this problem comes from recent work of Kenig and Merle who treated the case of spherically-symmetric solutions.
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Additional Information
  • Rowan Killip
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
  • Monica Visan
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
  • Received by editor(s): January 22, 2010
  • Received by editor(s) in revised form: June 14, 2010
  • Published electronically: January 28, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3893-3934
  • MSC (2010): Primary 35L71
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05400-0
  • MathSciNet review: 2775831