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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dispersion dynamics for the defocusing generalized Korteweg-de Vries equation
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by Stefan Steinerberger PDF
Proc. Amer. Math. Soc. 143 (2015), 789-800 Request permission

Abstract:

We study dispersion for the defocusing gKdV equation. It is expected that it is not possible for the bulk of the $L^2-$mass to concentrate in a small interval for a long time. We study a variance-type functional exploiting Tao’s monotonicity formula in the spirit of earlier work by Tao, as well as Kwon and Shao, and quantify its growth in terms of sublevel estimates.
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Additional Information
  • Stefan Steinerberger
  • Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
  • Address at time of publication: Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, Connecticut 06511
  • MR Author ID: 869041
  • ORCID: 0000-0002-7745-4217
  • Received by editor(s): May 3, 2013
  • Received by editor(s) in revised form: June 5, 2013
  • Published electronically: October 10, 2014
  • Additional Notes: The author was supported by a Hausdorff scholarship of the Bonn International Graduate School and was partially supported by SFB1060 of the DFG
  • Communicated by: Joachim Krieger
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 789-800
  • MSC (2010): Primary 37L50; Secondary 35Q53
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12285-4
  • MathSciNet review: 3283665