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Dispersive decay of small data solutions for the KdV equation

PDE and Applied Math Seminar

Speaker: Mihaela Ifrim, University of Wisconsin Madison
Related Webpage: https://www.math.wisc.edu/~ifrim/Home.html
Location: 2112 MSB
Start time: Fri, Mar 1 2019, 4:10PM

We consider the Korteweg-de Vries (KdV) equation, and prove that small localized data yields solutions which have dispersive decay on a quartic time-scale. This result is optimal, in view of the emergence of solitons at quartic time, as predicted by inverse scattering theory.