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Alex Himonas (University of Notre Dame)
Thursday 08 September 2022, 14:30-15:30
The Korteweg-de Vries equation on the half-line with smooth and rough data
- đ¤ Speaker: Alex Himonas (University of Notre Dame)
- đ Date & Time: Thursday 08 September 2022, 14:30 - 15:30
- đ Venue: Seminar Room 1, Newton Institute
Abstract
The well-posedness of the initial-boundary value problem (ibvp) for the Korteweg-de Vries equation on the half-line is studied for initial data in spatial Sobolev spaces $H^{s}(0, \infty)$, $s>-3/4$, and boundary data in thetemporal Sobolev spaces suggested by the time regularity of the Cauchy problem for the corresponding linear equation. First, linear estimates in Hadamard and Bourgain spaces are derived by utilizing the Fokas solution formula of the ibvp for the forced linear equation. Then, using these and the needed bilinear estimates, it is shown that the iteration map defined by the Fokas solution formula is a contraction in an appropriate solution space. This is based on work in collaboration with Athanassios Fokas, Dionyssis Mantzavinos and Fangchi Yan.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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