University of Heidelberg, Applied Analysis Seminar
Wed 09.06.2021
11:00, posted in Applied Analysis
Prof. Dr. Herbert Koch (U. Bonn)
The KdV hierarchy at low regularity
Online via Zoom

I will report on joint work with Friedrich Klaus and Baoping Liu on wellposedness for the full KdV hierarchy. The proof follows the scheme of recent work by Bringmann, Harrop-Griffith, Killip and Visan. We prove that wellposedness for the KdV equations is equivalent to wellposedness of the Gardner equations. Almost everything is based on a double expansion of the logarithm of the transmission coefficient in complex half planes, a central object of scattering theory. The first expansion is based on a Picard type iteration of the transmission coefficient, combined with combinatorical techniques for its logarithm. The second expansion is an expansion as asymptotic series. It gives access to conserved energies and higher equations.

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