Dispersion dynamics for the defocusing generalized Korteweg-de Vries equation

Steinerberger, Stefan

doi:10.1090/S0002-9939-2014-12285-4

Dispersion dynamics for the defocusing generalized Korteweg-de Vries equation
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by Stefan Steinerberger

Proc. Amer. Math. Soc. 143 (2015), 789-800

DOI: https://doi.org/10.1090/S0002-9939-2014-12285-4

Published electronically: October 10, 2014

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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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