# On the wellposedness of the KdV/KdV2 equations and their frequency maps

Kappeler, Thomas; Molnar, Jan-Cornelius (2018). On the wellposedness of the KdV/KdV2 equations and their frequency maps. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 35(1):101-160.

## Abstract

In form of a case study for the KdV and the KdV2 equations, we present a novel approach of representing the frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include convexity properties of the Hamiltonians and wellposedness results in spaces of low regularity. In particular, it is proved that on $H^S$ the KdV2 equation is $C^0$-wellposed if $s\geq0$ and illposed (in a strong sense) if $s<0$.

## Abstract

In form of a case study for the KdV and the KdV2 equations, we present a novel approach of representing the frequencies of integrable PDEs which allows to extend them analytically to spaces of low regularity and to study their asymptotics. Applications include convexity properties of the Hamiltonians and wellposedness results in spaces of low regularity. In particular, it is proved that on $H^S$ the KdV2 equation is $C^0$-wellposed if $s\geq0$ and illposed (in a strong sense) if $s<0$.

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## Additional indexing

Item Type: Journal Article, not_refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Mathematical Physics, Analysis English 2018 28 Mar 2018 08:39 19 Aug 2018 14:57 Elsevier 0294-1449 Closed Publisher DOI. An embargo period may apply. https://doi.org/10.1016/j.anihpc.2017.03.003

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