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Dispersion dynamics for the defocusing generalized Korteweg-de Vries equation


Author: Stefan Steinerberger
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
Published electronically: October 10, 2014
MathSciNet review: 3283665
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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

DOI: https://doi.org/10.1090/S0002-9939-2014-12285-4
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.