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Herbert Koch: The Korteweg–de Vries hierarchy at low regularity

Time: Tue 2023-10-31 15.00 - 16.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Herbert Koch, University of Bonn

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In this talk I report on joint work with Baoping Liu and Friedrich Klaus. We prove existence and uniqueness of weak solutions to all equations in the Gardner hierarchy for initial data in \(L^2(R)\). As a consequence we obtain uniqueness of weak solutions to all equations of the Korteweg–de Vries hierarchy for \(L^2(R)\) initial data and a continuous extension of the flows to \(H^1\).

The proof makes heavy use of the Miura map and of the commuting vector field method of Killip and Visan.