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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
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Mathematical Physics, Analysis
Language:English
Date:2018
Deposited On:28 Mar 2018 08:39
Last Modified:19 Aug 2018 14:57
Publisher:Elsevier
ISSN:0294-1449
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.anihpc.2017.03.003

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